{"id":154936,"date":"2022-03-26T00:05:18","date_gmt":"2022-03-25T18:35:18","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/coplanar-vectors-explanation-conditions-and-faqs\/"},"modified":"2024-12-13T13:53:56","modified_gmt":"2024-12-13T08:23:56","slug":"coplanar-vectors-explanation-conditions-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/","title":{"rendered":"Coplanar Vectors \u2013 Explanation, Conditions and FAQs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#Coplanar_Vectors_Introduction\" title=\"Coplanar Vectors Introduction\">Coplanar Vectors Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#All_about_Coplanar_Vectors\" title=\"All about Coplanar Vectors\">All about Coplanar Vectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#Equality_of_Vectors\" title=\"Equality of Vectors\">Equality of Vectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#Types_of_Vectors\" title=\"Types of Vectors\">Types of Vectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#Coplanarity_in_Theory_and_Practice\" title=\"Coplanarity in Theory and Practice\">Coplanarity in Theory and Practice<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#Theory\" title=\"Theory\">Theory<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#Practice\" title=\"Practice\">Practice<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#Conditions_for_Coplanar_Vectors_Properties_of_Coplanar_Vectors\" title=\"Conditions for Coplanar Vectors\/ Properties of Coplanar Vectors\">Conditions for Coplanar Vectors\/ Properties of Coplanar Vectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#What_are_Linearly_Independent_Vectors\" title=\"What are Linearly Independent Vectors?\">What are Linearly Independent Vectors?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#What_are_Linearly_Dependent_Vectors\" title=\"What are Linearly Dependent Vectors?\">What are Linearly Dependent Vectors?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#How_do_you_Know_if_Two_Vectors_are_Coplanar\" title=\"How do you Know if Two Vectors are Coplanar?\">How do you Know if Two Vectors are Coplanar?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/#FAQs\" title=\"FAQs\">FAQs<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Coplanar_Vectors_Introduction\"><\/span>Coplanar Vectors Introduction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Coplanar Vectors: A<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanar-vectors\/\"> coplanar vector<\/a> is a vector that is located in the same plane as another vector. This is often done for convenience when working with vectors, as it makes calculations and manipulations simpler. In physics, a vector is a mathematical representation of a physical quantity, such as force or momentum. Vectors can be added, subtracted, and multiplied together, and they have a direction and a magnitude.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154935 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/coplanar-vectors-explanation-conditions-and-faqs.jpg\" alt=\"Coplanar Vectors \u2013 Explanation, Conditions and FAQs\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/coplanar-vectors-explanation-conditions-and-faqs.jpg?v=1648233314 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/coplanar-vectors-explanation-conditions-and-faqs-300x212.jpg?v=1648233314 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"All_about_Coplanar_Vectors\"><\/span>All about Coplanar Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A coplanar vector is a vector that lies in the same plane as another vector. In other words, the two vectors are parallel to each other. This can easily visualized using a two-dimensional plane. If two vectors are drawn on the plane, and they lie in the same line, then they are coplanar vectors.<\/p>\n<p>The magnitude of a coplanar vector is simply the sum of the magnitudes of the individual vectors. The direction of a coplanar vector is the same as the direction of the individual vectors.<\/p>\n<p>Coplanar vectors are often used in physics and engineering. For example, they can used to model the forces between objects.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equality_of_Vectors\"><\/span>Equality of Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Two vectors said to equal if they have the same magnitude and direction.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Vectors\"><\/span>Types of Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are three types of vectors: magnitude, direction, and displacement vectors.<\/p>\n<ul>\n<li>A magnitude vector is simply the magnitude (or size) of a vector. It has no direction information.<\/li>\n<li>A direction vector has both magnitude and direction information. It points in a specific direction.<\/li>\n<li>A displacement vector has magnitude and direction information, and it also has a starting point and an ending point. It shows the displacement between the two points.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Coplanarity_in_Theory_and_Practice\"><\/span>Coplanarity in Theory and Practice<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Theory\"><\/span>Theory<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In theory, coplanarity is the condition of being on the same plane. Therefore this means that all of the features on a part are at the same height and that there are no gaps or overlaps between them.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Practice\"><\/span>Practice<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>In practice, coplanarity is often difficult to achieve. This is because it is often difficult to measure and to maintain the same height across a variety of features. Even slight variations can cause problems with fit and assembly.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Conditions_for_Coplanar_Vectors_Properties_of_Coplanar_Vectors\"><\/span>Conditions for Coplanar Vectors\/ Properties of Coplanar Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Two vectors said to be coplanar if they lie in the same plane.<\/p>\n<p>If vectors A and B are coplanar, then they have the following properties:<\/p>\n<ul>\n<li>Their sum is a vector in the same plane as A and B.<\/li>\n<li>difference is a vector in the same plane as A and B.<\/li>\n<li>Their product is a vector in the same plane as A and B.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Linearly_Independent_Vectors\"><\/span>What are Linearly Independent Vectors?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Linearly independent vectors are vectors that can written as a linear combination of each other, but not all linear combinations of vectors are independent.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Linearly_Dependent_Vectors\"><\/span>What are Linearly Dependent Vectors?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Linearly dependent vectors are vectors that related to each other in a way that one vector can expressed as a combination of the other vectors.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_do_you_Know_if_Two_Vectors_are_Coplanar\"><\/span>How do you Know if Two Vectors are Coplanar?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If two vectors are coplanar, then they will have the same orientation and lie in the same plane.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>&nbsp;<\/p>\n<p>Q: What are coplanar vectors?<br \/>\nA: Coplanar vectors are vectors that lie in the same plane.<\/p>\n<p>Q: How can you tell if two vectors are coplanar?<br \/>\nA: Two vectors are coplanar if there exists a plane that contains both of them.<\/p>\n<p>Q: What is the cross product of two coplanar vectors?<br \/>\nA: The cross product of two coplanar vectors is a vector perpendicular to the plane in which they lie.<\/p>\n<p>Q: Can three non-collinear vectors be coplanar?<br \/>\nA: No, three non-collinear vectors cannot be coplanar because they span a three-dimensional space.<\/p>\n<p>Q: What is the scalar triple product of three coplanar vectors?<br \/>\nA: The scalar triple product of three coplanar vectors is zero, since the three vectors lie in the same plane.<\/p>\n<p>Q: How many coplanar vectors are needed to define a plane?<br \/>\nA: Two non-collinear coplanar vectors are needed to define a plane.<\/p>\n<p>Q: What is the angle between two coplanar vectors?<br \/>\nA: The angle between two coplanar vectors is the angle between the two lines they define in the plane they lie in.<\/p>\n<p>Q: Can two collinear vectors be coplanar?<br \/>\nA: Yes, two collinear vectors are coplanar since they lie on the same line which can be considered as a plane.<\/p>\n<p>Q: What is the projection of one coplanar vector onto another?<br \/>\nA: The projection of one coplanar vector onto another is the component of the first vector that lies in the direction of the second vector.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Coplanar Vectors Introduction Coplanar Vectors: A coplanar vector is a vector that is located in the same plane as another [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Coplanar Vectors","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about coplanar vectors topic of maths in details explained by subject experts on infinitylearn.com. 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