{"id":153950,"date":"2022-03-25T22:59:34","date_gmt":"2022-03-25T17:29:34","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/coplanarity-of-vectors-explanation-definition-types-examples-conditions-applications\/"},"modified":"2022-12-31T17:17:30","modified_gmt":"2022-12-31T11:47:30","slug":"coplanarity-of-vectors-explanation-definition-types-examples-conditions-applications","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/coplanarity-of-vectors\/","title":{"rendered":"Coplanarity of Vectors &#8211; Explanation, Definition, Types, Examples, Conditions, Applications"},"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\/coplanarity-of-vectors\/#What_are_Vectors_and_What_is_Coplanarity_of_Vectors\" title=\"What are Vectors and What is Coplanarity of Vectors?\">What are Vectors and What is Coplanarity of Vectors?<\/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\/coplanarity-of-vectors\/#Linearly_Dependent_and_Independent_Vectors\" title=\"Linearly Dependent and Independent Vectors:\">Linearly Dependent and Independent 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\/coplanarity-of-vectors\/#Linearly_Independent_Vectors\" title=\"Linearly Independent Vectors:\">Linearly Independent 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\/coplanarity-of-vectors\/#Linearly_Dependent_Vectors\" title=\"Linearly Dependent Vectors:\">Linearly Dependent 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\/coplanarity-of-vectors\/#Application_of_Vectors\" title=\"Application of Vectors:\">Application of Vectors:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanarity-of-vectors\/#Types_and_Examples_of_Vector\" title=\"Types and Examples of Vector\">Types and Examples of Vector<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanarity-of-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-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanarity-of-vectors\/#What_are_Coplanar_Vectors\" title=\"What are Coplanar Vectors?\">What are 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\/coplanarity-of-vectors\/#Coplanar_Vectors_Definition\" title=\"Coplanar Vectors Definition\">Coplanar Vectors Definition<\/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\/coplanarity-of-vectors\/#Examples_of_Coplanar_Vectors\" title=\"Examples of Coplanar Vectors\">Examples of Coplanar 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\/coplanarity-of-vectors\/#Points_to_Look_for_on_Coplanar_Vectors\" title=\"Points to Look for on Coplanar Vectors:\">Points to Look for on Coplanar Vectors:<\/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\/coplanarity-of-vectors\/#Coplanar_Vectors_Requirements\" title=\"Coplanar Vectors&#8217; Requirements\">Coplanar Vectors&#8217; Requirements<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/coplanarity-of-vectors\/#Uses_of_Coplanar_Vectors\" title=\"Uses of Coplanar Vectors\">Uses of Coplanar Vectors<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Vectors_and_What_is_Coplanarity_of_Vectors\"><\/span>What are Vectors and What is Coplanarity of Vectors?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A vector is a mathematical quantity that has both magnitude and direction. Two vectors are said to be coplanar if they lie in the same plane.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153949 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/coplanarity-of-vectors-explanation-definition-types-examples-conditions-applications.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/coplanarity-of-vectors-explanation-definition-types-examples-conditions-applications.jpg?v=1648229371 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/coplanarity-of-vectors-explanation-definition-types-examples-conditions-applications-300x212.jpg?v=1648229371 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linearly_Dependent_and_Independent_Vectors\"><\/span>Linearly Dependent and Independent Vectors:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A vector is said to be linearly dependent on a second vector if the first vector can be expressed as a linear combination of the second vector and some other vector(s). A vector is said to be linearly independent of a second vector if the first vector cannot be expressed as a linear combination of the second vector and any other vector(s).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linearly_Independent_Vectors\"><\/span>Linearly Independent Vectors:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A vector is linearly independent if it can be expressed as a linear combination of the other vectors in the set, but cannot be expressed as a combination of any other two vectors in the set. In other words, a vector is linearly independent if its components are not all zero.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linearly_Dependent_Vectors\"><\/span>Linearly Dependent Vectors:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>When vectors are linearly dependent, they cannot be represented as a unique linear combination of each other. In other words, at least one of the vectors can be expressed as a linear combination of the other vectors.<\/p>\n<p>For example, the vectors $\\vec{a}, \\vec{b}, \\vec{c}$ are linearly dependent, because the vector $\\vec{c}$ can be expressed as a linear combination of the other two vectors:<\/p>\n<p>$$\\vec{c} = \\vec{a} + \\vec{b}$$<\/p>\n<p>On the other hand, the vectors $\\vec{a}, \\vec{b}, \\vec{d}$ are linearly independent, because the vector $\\vec{d}$ cannot be expressed as a linear combination of the other two vectors.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Application_of_Vectors\"><\/span>Application of Vectors:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are many different applications for vectors. Some common applications are in physics, engineering, and mathematics.<\/p>\n<p>In physics, vectors are used to describe the motion of objects. In engineering, vectors are used to calculate the forces on objects. In mathematics, vectors are used to solve problems.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_and_Examples_of_Vector\"><\/span>Types and Examples of Vector<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Fields<\/p>\n<p>A vector field is a mathematical representation of a physical phenomenon in which each point in space is associated with a vector. Vector fields can be used to model a variety of physical phenomena, including electric and magnetic fields, fluid flow, and heat flow.<\/p>\n<p>Some common types of vector fields include:<\/p>\n<p>\u2022 Electric field: A vector field that describes the electric force between two points.<\/p>\n<p>\u2022 Magnetic field: A vector field that describes the magnetic force between two points.<\/p>\n<p>\u2022 Fluid flow: A vector field that describes the motion of a fluid.<\/p>\n<p>\u2022 Heat flow: A vector field that describes the flow of heat.<\/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<p>A magnitude vector is a vector that has magnitude only. It has no direction.<\/p>\n<p>A direction vector is a vector that has magnitude and direction.<\/p>\n<p>A displacement vector is a vector that has magnitude and direction. It also has a starting point and an end point.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_are_Coplanar_Vectors\"><\/span>What are Coplanar Vectors?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Coplanar vectors are two or more vectors that lie in the same plane.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Coplanar_Vectors_Definition\"><\/span>Coplanar Vectors Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In mathematics, two vectors are said to be coplanar if they lie in the same plane.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Examples_of_Coplanar_Vectors\"><\/span>Examples of Coplanar Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A vector is said to be coplanar if it lies in the same plane as some other vector. In the diagram below, vectors A and B are both coplanar.<\/p>\n<p>Vector A is in the same plane as vector B.<\/p>\n<p>Vector A is not in the same plane as vector C.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Points_to_Look_for_on_Coplanar_Vectors\"><\/span>Points to Look for on Coplanar Vectors:<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>1. The vectors are perpendicular to each other.<\/p>\n<p>2. The vectors are of the same magnitude.<\/p>\n<p>3. The vectors are of the same direction.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Coplanar_Vectors_Requirements\"><\/span>Coplanar Vectors&#8217; Requirements<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Two vectors are said to be coplanar if they are both contained within the same plane. In order for two vectors to be coplanar, they must satisfy the following requirements:<\/p>\n<p>The vectors must be linearly independent.<\/p>\n<p>The vectors must be of the same magnitude.<\/p>\n<p>The vectors must be of the same direction.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Uses_of_Coplanar_Vectors\"><\/span>Uses of Coplanar Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are several ways to use coplanar vectors. One way is to use them to calculate the magnitude and direction of a resultant vector. Another way is to use them to calculate the magnitude and direction of a force.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What are Vectors and What is Coplanarity of Vectors? A vector is a mathematical quantity that has both magnitude and [&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":"Coplanarity of Vectors","_yoast_wpseo_title":"Coplanarity of Vectors - Explanation, Definition, Types, Examples","_yoast_wpseo_metadesc":"Learn about coplanarity of vectors topic of maths in details explained by subject experts on infinitylearn.com. 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