{"id":26402,"date":"2023-03-15T10:17:23","date_gmt":"2023-03-15T10:17:23","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26402"},"modified":"2024-04-02T05:42:08","modified_gmt":"2024-04-02T05:42:08","slug":"coplanar-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar","title":{"rendered":"Coplanar &#8211; Definition With Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-48762d7f-0b0d-47be-8b44-35154dce4c84\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar#0-what-does-coplanar-mean-in-geometry>What Does Coplanar Mean in Geometry?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar#2-what-is-the-difference-between-collinear-and-coplanar>What Is the Difference Between Collinear and Coplanar?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar#3-what-are-coplanar-and-non-coplanar-points>What Are Coplanar and Non-coplanar Points?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar#11-solved-examples-on-%E2%80%9Ccoplanar%E2%80%9D>Solved Examples on \u201cCoplanar\u201d<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar#12-practice-problems-on-%E2%80%9Ccoplanar%E2%80%9D>Practice Problems on \u201cCoplanar\u201d<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar#13-frequently-asked-questions-on-%E2%80%9Ccoplanar%E2%80%9D>Frequently Asked Questions on \u201cCoplanar\u201d<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-does-coplanar-mean-in-geometry\">What Does Coplanar Mean in Geometry?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Coplanar simply means \u201clying on the same plane.\u201d Here, \u201cco\u201d means \u201ctogether,\u201d and \u201cplanar\u201d means \u201clying on a plane.\u201d<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In geometry, a plane is a two-dimensional, flat surface that extends infinitely in both dimensions.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"491\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/a-plane.png\" alt=\"A plane\" class=\"wp-image-41475\" title=\"A plane\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/a-plane.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/a-plane-300x237.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When two or more points or lines lie on the same plane or common plane, they are said to be coplanar.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now you might be wondering, what does non-coplanar mean? It is simply the opposite of coplanar and means \u201cnot lying on the same plane.\u201d<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-coplanar-definition\">Coplanar: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Any geometric object or shape such as a line, point is said to be coplanar if they lie on the same plane. Otherwise, they are called non-coplanar.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: Points P, Q, R, S lie in the same plane. So, they are coplanar.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"369\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-points-p-q-r-and-s.png\" alt=\"Coplanar points P, Q, R, and S\" class=\"wp-image-41476\" title=\"Coplanar points P, Q, R, and S\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-points-p-q-r-and-s.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-points-p-q-r-and-s-300x178.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-what-is-the-difference-between-collinear-and-coplanar\">What Is the Difference Between Collinear and Coplanar?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Collinear simply means lying on the same line. Coplanar means to exist on the same plane.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Collinear points lie on the same line. If points are collinear, they are also coplanar. However, coplanar points are not necessarily collinear.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"357\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-points-and-collinear-points.png\" alt=\"Coplanar points and Collinear points\" class=\"wp-image-41477\" title=\"Coplanar points and Collinear points\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-points-and-collinear-points.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-points-and-collinear-points-300x172.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the points A, B, C, and D are four coplanar points. However, they are not collinear. The points P, Q, R are collinear and thus also coplanar.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The concept of coplanar vs. non-coplanar points or coplanar vs. non-coplanar lines is quite intuitive. Let\u2019s explore in detail.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-what-are-coplanar-and-non-coplanar-points\">What Are Coplanar and Non-coplanar Points?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s understand the definition of coplanar points and non-coplanar points with examples.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-coplanar-points-definition\">Coplanar Points: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Points that lie on the same plane are \u201ccoplanar points.\u201d&nbsp;<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-non-coplanar-points-definition\">Non-coplanar Points: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Points that do not lie on the same plane are \u201cnon-coplanar points.\u201d<\/strong><\/p>\n\n\n<div class=\"ub-styled-box ub-notification-box custom-callout_box\" id=\"ub-styled-box-46a464b7-a86f-4ea7-a89e-5865ea84a0f9\">\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Important Note:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know that a line passes through any two given points. Thus, two points in a two-dimensional plane can always pass through a line and hence any two points are collinear (and thereby coplanar). Similarly, three points can always pass through a plane and hence any 3 points are always coplanar. Thus, we can say that four or more points that lie on the same plane are known as coplanar points.<\/p>\n\n\n<\/div>\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"611\" height=\"341\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-and-non-coplanar-points-example.png\" alt=\"Coplanar and non-coplanar points example\" class=\"wp-image-41478\" title=\"Coplanar and non-coplanar points example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-and-non-coplanar-points-example.png 611w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-and-non-coplanar-points-example-300x167.png 300w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The points A, B, and C lie on the same plane.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">They are coplanar.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Point D lies outside the plane.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It is not coplanar with the points A, B, and C.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">However, if you choose any three points at random, they will be coplanar since a plane can be drawn through any three points.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By this logic, the points A, B, D are coplanar.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Points B, C, D are coplanar, and so on.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-what-are-coplanar-and-non-coplanar-lines-in-geometry\">What Are Coplanar and Non-coplanar Lines in Geometry?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s understand the definition of coplanar lines and non-coplanar lines using an example.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"613\" height=\"582\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-and-non-coplanar-lines-on-a-cube.png\" alt=\"Coplanar and non-coplanar lines on a cube\" class=\"wp-image-41479\" title=\"Coplanar and non-coplanar lines on a cube\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-and-non-coplanar-lines-on-a-cube.png 613w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/04\/coplanar-and-non-coplanar-lines-on-a-cube-300x285.png 300w\" sizes=\"auto, (max-width: 613px) 100vw, 613px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-coplanar-lines-definition\">Coplanar Lines: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When two or more than two lines lie on the same plane, those lines are said to be coplanar lines.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the given cube, some examples of coplanar lines are as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">EF and GH are coplanar lines.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">AD and DH are coplanar lines.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">They reside on the same face of the cube.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"8-non-coplanar-lines-definition\">Non-coplanar Lines Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When the lines do not lie on the same plane, they are called non-coplanar lines.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In the cube, some examples of non-coplanar lines are:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Lines AB, FG are non-coplanar.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Lines EF, CD are non-coplanar lines as they do not reside on the same face of the cube, i.e., not on the same plane.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-facts\">Facts<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Any two points are always going to be coplanar.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Any three points you take will always be coplanar.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Four or more points are said to be coplanar if they are all present on one plane.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Two lines whose one endpoint meet are coplanar by nature.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Two parallel lines are always coplanar.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article we learned about collinear and coplanar points, their definition in geometry, coplanar and non-coplanar lines, methods to find if 4 points are coplanar or not, then we looked at how we can determine if two lines are coplanar.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-solved-examples-on-%E2%80%9Ccoplanar%E2%80%9D\">Solved Examples on \u201cCoplanar\u201d<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. A point A, which has the coordinates <\/strong>$(3, \\;-2, 4)$<strong> lies on a plane surface having the equation&nbsp; <\/strong>$x \\;-\\; 4y + 2z\\;-\\;k = 0$<strong>. Find the value of k.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since A is coplanar or lies on the plane surface, it must satisfy the given equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find k, put the coordinates in place of x, y and z.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x \\;-\\;4y + 2z\\;-\\;k = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3\\;-\\;4(\\;-2) + 2(4) \\;-\\;k = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3 + 8 + 8 \\;-\\; k = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$19\\;-\\;k = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$k = 19$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. A set of points lie on the same line. Are they coplanar?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A set of points lying on the same line are called collinear points. If points are collinear, they are also coplanar. Thus, the points are also coplanar.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3<\/strong><strong>. <\/strong><strong>Determine if coplanar or not: (i) Hands of an analog clock, (ii) Paint drops on a canvas.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(i) The hands of an analog clock always lie and move on the same background plane of the clock, they are coplanar.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(ii) Paint drops can be considered points on a painting canvas, which is a 2D plane. So, they are coplanar points.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. <\/strong><strong>What do you mean by non-coplanar lines? Give a real world example.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution<\/strong><strong>:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Non-coplanar lines are two or more lines which do not reside on the same geometrical plane. They are non-intersecting and do not satisfy the condition that the vector determinant should be zero.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">One real world example of non-coplanar lines can be lines on the floor and lines on the wall of a room.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-practice-problems-on-%E2%80%9Ccoplanar%E2%80%9D\">Practice Problems on \u201cCoplanar\u201d<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Coplanar \u2013 Definition With Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The lines PQ and UV are _______.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-1-2.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">Coplanar<\/div><div class=\"spq_answer_block\" data-value=\"1\">Non-coplanar<\/div><div class=\"spq_answer_block\" data-value=\"2\">Parallel<\/div><div class=\"spq_answer_block\" data-value=\"3\">Intersecting<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Non-coplanar<br\/>The lines do not lie on the same face of the cube. So, they are not coplanar.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Points A, F, B are _____<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-2-2.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">Collinear<\/div><div class=\"spq_answer_block\" data-value=\"1\">Non-coplanar<\/div><div class=\"spq_answer_block\" data-value=\"2\">Coplanar<\/div><div class=\"spq_answer_block\" data-value=\"3\">Both a and c<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Both a and c<br\/>Points A, F, B are collinear and thus coplanar.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">A point A which has the coordinates $(4, 5, \\;-\\;1)$ lies on the plane having the equation $2x\\;-\\;y + 5z\\;-\\;k = 0$. What is the value of k?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-\\;3$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-\\;2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$2$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $-\\;2$<br\/>Since A is coplanar or exists on the plane surface, it must satisfy the given equation.<br>\r\nTo find k, put the coordinates in place of x, y and z.<br>\r\n$2x \\;-\\; y + 5z \\;-\\; k = 0$\tfor A$(4, 5, \\;-\\;1)$<br>\r\n$2(4)\\;-\\;5 + 5 (\\;-1)\\;-\\;k = 0$<br>\r\n$8\\;-\\;5\\;-\\;5\\;-\\;k = 0$<br>\r\n$\\;-\\;2 \\;-\\; k = 0$<br>\r\n$k = \\;-\\;2$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Any three points in a three-dimensional space are ____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Collinear<\/div><div class=\"spq_answer_block\" data-value=\"1\">Non coplanar<\/div><div class=\"spq_answer_block\" data-value=\"2\">Coplanar<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Coplanar<br\/>Any three points are always coplanar since you can have a plane passing through them.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Coplanar \u2013 Definition With Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Coplanar\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The lines PQ and UV are _______.\",\n                    \"text\": \"The lines PQ and UV are _______. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-1-2.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The lines do not lie on the same face of the cube. So, they are not coplanar.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Coplanar\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The lines do not lie on the same face of the cube. So, they are not coplanar.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Parallel\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The lines do not lie on the same face of the cube. So, they are not coplanar.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Intersecting\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The lines do not lie on the same face of the cube. So, they are not coplanar.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Non-coplanar\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The lines do not lie on the same face of the cube. So, they are not coplanar.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The lines do not lie on the same face of the cube. So, they are not coplanar.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Points A, F, B are _____\",\n                    \"text\": \"Points A, F, B are _____ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Practice-Problems-2-2.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Points A, F, B are collinear and thus coplanar.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Collinear\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Points A, F, B are collinear and thus coplanar.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Non-coplanar\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Points A, F, B are collinear and thus coplanar.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Coplanar\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Points A, F, B are collinear and thus coplanar.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Both a and c\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Points A, F, B are collinear and thus coplanar.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Points A, F, B are collinear and thus coplanar.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A point A which has the coordinates $$(4, 5, \\\\;-\\\\;1)$$ lies on the plane having the equation $$2x\\\\;-\\\\;y + 5z\\\\;-\\\\;k = 0$$. What is the value of k?\",\n                    \"text\": \"A point A which has the coordinates $$(4, 5, \\\\;-\\\\;1)$$ lies on the plane having the equation $$2x\\\\;-\\\\;y + 5z\\\\;-\\\\;k = 0$$. What is the value of k?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Since A is coplanar or exists on the plane surface, it must satisfy the given equation.<br>\r\nTo find k, put the coordinates in place of x, y and z.<br>\r\n$$2x \\\\;-\\\\; y + 5z \\\\;-\\\\; k = 0$$\tfor A$$(4, 5, \\\\;-\\\\;1)$$<br>\r\n$$2(4)\\\\;-\\\\;5 + 5 (\\\\;-1)\\\\;-\\\\;k = 0$$<br>\r\n$$8\\\\;-\\\\;5\\\\;-\\\\;5\\\\;-\\\\;k = 0$$<br>\r\n$$\\\\;-\\\\;2 \\\\;-\\\\; k = 0$$<br>\r\n$$k = \\\\;-\\\\;2$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since A is coplanar or exists on the plane surface, it must satisfy the given equation.<br>\r\nTo find k, put the coordinates in place of x, y and z.<br>\r\n$$2x \\\\;-\\\\; y + 5z \\\\;-\\\\; k = 0$$\tfor A$$(4, 5, \\\\;-\\\\;1)$$<br>\r\n$$2(4)\\\\;-\\\\;5 + 5 (\\\\;-1)\\\\;-\\\\;k = 0$$<br>\r\n$$8\\\\;-\\\\;5\\\\;-\\\\;5\\\\;-\\\\;k = 0$$<br>\r\n$$\\\\;-\\\\;2 \\\\;-\\\\; k = 0$$<br>\r\n$$k = \\\\;-\\\\;2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-\\\\;3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since A is coplanar or exists on the plane surface, it must satisfy the given equation.<br>\r\nTo find k, put the coordinates in place of x, y and z.<br>\r\n$$2x \\\\;-\\\\; y + 5z \\\\;-\\\\; k = 0$$\tfor A$$(4, 5, \\\\;-\\\\;1)$$<br>\r\n$$2(4)\\\\;-\\\\;5 + 5 (\\\\;-1)\\\\;-\\\\;k = 0$$<br>\r\n$$8\\\\;-\\\\;5\\\\;-\\\\;5\\\\;-\\\\;k = 0$$<br>\r\n$$\\\\;-\\\\;2 \\\\;-\\\\; k = 0$$<br>\r\n$$k = \\\\;-\\\\;2$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since A is coplanar or exists on the plane surface, it must satisfy the given equation.<br>\r\nTo find k, put the coordinates in place of x, y and z.<br>\r\n$$2x \\\\;-\\\\; y + 5z \\\\;-\\\\; k = 0$$\tfor A$$(4, 5, \\\\;-\\\\;1)$$<br>\r\n$$2(4)\\\\;-\\\\;5 + 5 (\\\\;-1)\\\\;-\\\\;k = 0$$<br>\r\n$$8\\\\;-\\\\;5\\\\;-\\\\;5\\\\;-\\\\;k = 0$$<br>\r\n$$\\\\;-\\\\;2 \\\\;-\\\\; k = 0$$<br>\r\n$$k = \\\\;-\\\\;2$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-\\\\;2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Since A is coplanar or exists on the plane surface, it must satisfy the given equation.<br>\r\nTo find k, put the coordinates in place of x, y and z.<br>\r\n$$2x \\\\;-\\\\; y + 5z \\\\;-\\\\; k = 0$$\tfor A$$(4, 5, \\\\;-\\\\;1)$$<br>\r\n$$2(4)\\\\;-\\\\;5 + 5 (\\\\;-1)\\\\;-\\\\;k = 0$$<br>\r\n$$8\\\\;-\\\\;5\\\\;-\\\\;5\\\\;-\\\\;k = 0$$<br>\r\n$$\\\\;-\\\\;2 \\\\;-\\\\; k = 0$$<br>\r\n$$k = \\\\;-\\\\;2$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Since A is coplanar or exists on the plane surface, it must satisfy the given equation.<br>\r\nTo find k, put the coordinates in place of x, y and z.<br>\r\n$$2x \\\\;-\\\\; y + 5z \\\\;-\\\\; k = 0$$\tfor A$$(4, 5, \\\\;-\\\\;1)$$<br>\r\n$$2(4)\\\\;-\\\\;5 + 5 (\\\\;-1)\\\\;-\\\\;k = 0$$<br>\r\n$$8\\\\;-\\\\;5\\\\;-\\\\;5\\\\;-\\\\;k = 0$$<br>\r\n$$\\\\;-\\\\;2 \\\\;-\\\\; k = 0$$<br>\r\n$$k = \\\\;-\\\\;2$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Any three points in a three-dimensional space are ____.\",\n                    \"text\": \"Any three points in a three-dimensional space are ____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Any three points are always coplanar since you can have a plane passing through them.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Collinear\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Any three points are always coplanar since you can have a plane passing through them.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Non coplanar\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Any three points are always coplanar since you can have a plane passing through them.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Any three points are always coplanar since you can have a plane passing through them.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Coplanar\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Any three points are always coplanar since you can have a plane passing through them.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Any three points are always coplanar since you can have a plane passing through them.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-frequently-asked-questions-on-%E2%80%9Ccoplanar%E2%80%9D\">Frequently Asked Questions on \u201cCoplanar\u201d<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-cca463b1-32f3-4400-a5c8-17abad6778c0\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-cca463b1-32f3-4400-a5c8-17abad6778c0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cca463b1-32f3-4400-a5c8-17abad6778c0\"><strong>Are coplanar points also collinear?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-cca463b1-32f3-4400-a5c8-17abad6778c0\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Collinear points are always coplanar, but coplanar points need not be collinear.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-cca463b1-32f3-4400-a5c8-17abad6778c0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cca463b1-32f3-4400-a5c8-17abad6778c0\"><strong>Are collinear points also coplanar?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-cca463b1-32f3-4400-a5c8-17abad6778c0\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, two or more collinear points are always coplanar. When there are multiple points residing on a line, and if we make a plane which goes through that line, the points will automatically reside on the plane, making them coplanar.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-cca463b1-32f3-4400-a5c8-17abad6778c0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cca463b1-32f3-4400-a5c8-17abad6778c0\"><strong>Give some examples of coplanar points.<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-cca463b1-32f3-4400-a5c8-17abad6778c0\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Almost all the endpoints of a two-dimensional figure are coplanar. In three-dimensional form, the endpoints of one face of a cube can be considered coplanar.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-cca463b1-32f3-4400-a5c8-17abad6778c0\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cca463b1-32f3-4400-a5c8-17abad6778c0\"><strong>Can the X and Y axes of the cartesian plane be considered coplanar?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-cca463b1-32f3-4400-a5c8-17abad6778c0\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Both axes intersect each other at right angles. So, these axes can be considered coplanar.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Does Coplanar Mean in Geometry? Coplanar simply means \u201clying on the same plane.\u201d Here, \u201cco\u201d means \u201ctogether,\u201d and \u201cplanar\u201d means \u201clying on a plane.\u201d In geometry, a plane is a two-dimensional, flat surface that extends infinitely in both dimensions.&nbsp; When two or more points or lines lie on the same plane or common plane, &#8230; <a title=\"Coplanar &#8211; Definition With Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/coplanar\" aria-label=\"More on Coplanar &#8211; Definition With Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26402","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26402","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=26402"}],"version-history":[{"count":24,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26402\/revisions"}],"predecessor-version":[{"id":41480,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26402\/revisions\/41480"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26402"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26402"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}