{"id":156266,"date":"2022-03-26T01:33:58","date_gmt":"2022-03-25T20:03:58","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/calculate-vector-product-definition-properties-and-examples\/"},"modified":"2022-12-22T21:37:51","modified_gmt":"2022-12-22T16:07:51","slug":"calculate-vector-product-definition-properties-and-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/calculate-vector-product\/","title":{"rendered":"Calculate Vector Product \u2013 Definition, Properties and Examples"},"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\/calculate-vector-product\/#Vector_Product\" title=\"Vector Product\">Vector Product<\/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\/calculate-vector-product\/#Define_Vector_Product\" title=\"Define Vector Product\">Define Vector Product<\/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\/calculate-vector-product\/#Properties_Of_Vector_Product\" title=\"Properties Of Vector Product\">Properties Of Vector Product<\/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\/calculate-vector-product\/#Cross_Vector_Product_Of_Two_Parallel_Vectors\" title=\"Cross Vector Product Of Two Parallel Vectors\">Cross Vector Product Of Two Parallel 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\/calculate-vector-product\/#Cross_Vector_Product_Of_Two_Parallel_Vectors_In_Cartesian_Form\" title=\"Cross Vector Product Of Two Parallel Vectors In Cartesian Form\">Cross Vector Product Of Two Parallel Vectors In Cartesian Form<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Vector_Product\"><\/span>Vector Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The vector product, also known as the cross product, is a mathematical operation that takes two vectors and produces a third vector. The vector product is denoted by the symbol \u00d7, and is defined as follows:<\/p>\n<p>Where A and B are vectors, and c is a vector.<\/p>\n<p>The vector product is associative, meaning that the order of the vectors does not affect the result:<\/p>\n<p>A \u00d7 (B \u00d7 C) = (A \u00d7 B) \u00d7 C.<\/p>\n<p>The vector product is also commutative:<\/p>\n<p>A \u00d7 B = B \u00d7 A.<\/p>\n<p>The vector product is distributive:<\/p>\n<p>A \u00d7 (B + C) = (A \u00d7 B) + (A \u00d7 C).<\/p>\n<p>The vector product is zero if and only if the vectors are parallel:<\/p>\n<p>A \u00d7 B = 0 if and only if A = B.<\/p>\n<p>The vector product is perpendicular to both of the vectors that are involved in it:<\/p>\n<p>A \u00d7 B is perpendicular to both A and B.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156265 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/calculate-vector-product-definition-properties-and-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/calculate-vector-product-definition-properties-and-examples.jpg?v=1648238635 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/calculate-vector-product-definition-properties-and-examples-300x212.jpg?v=1648238635 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Define_Vector_Product\"><\/span>Define Vector Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A vector product is a vector in mathematics that is defined as the cross product of two other vectors. This vector is perpendicular to both of the original vectors and is determined by the magnitudes of the vectors and the angle between them. The vector product is a useful tool for solving problems in physics and engineering<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_Of_Vector_Product\"><\/span>Properties Of Vector Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The vector product is a mathematical operation that takes two vectors and produces a third vector. The vector product is also called the cross product.<\/p>\n<p>The vector product is defined as follows:<\/p>\n<p>The vector product is distributive.<\/p>\n<p>The vector product is associative.<\/p>\n<p>The vector product is commutative.<\/p>\n<p>The vector product is Lorentz invariant.<\/p>\n<p>The vector product is a binary operation.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cross_Vector_Product_Of_Two_Parallel_Vectors\"><\/span>Cross Vector Product Of Two Parallel Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A cross product of two vectors is a vector that is perpendicular to both of the input vectors. This vector is found by taking the product of the length of the first vector and the sin of the angle between the two vectors, and then multiplying that by the length of the second vector.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cross_Vector_Product_Of_Two_Parallel_Vectors_In_Cartesian_Form\"><\/span>Cross Vector Product Of Two Parallel Vectors In Cartesian Form<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The cross vector product of two parallel vectors is a vector perpendicular to both of the original vectors. It is calculated by multiplying the magnitude of the first vector by the magnitude of the second vector and then dividing by the product of their magnitudes<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vector Product The vector product, also known as the cross product, is a mathematical operation that takes two vectors 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":"Calculate Vector Product \u2013 Definition, Properties and Examples","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Calculate Vector Product topic of Maths in details explained by subject experts on infinitylearn.com. 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