{"id":153802,"date":"2022-03-25T22:49:41","date_gmt":"2022-03-25T17:19:41","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/dot-product-geometric-definition-concept-algebraic-definition-properties-formula-solved-examples-and-faqs\/"},"modified":"2022-12-31T17:31:01","modified_gmt":"2022-12-31T12:01:01","slug":"dot-product-geometric-definition-concept-algebraic-definition-properties-formula-solved-examples-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/dot-product\/","title":{"rendered":"Dot Product &#8211; Geometric Definition, Concept, Algebraic Definition, Properties, Formula, Solved Examples, 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\/dot-product\/#What_is_Dot_Product\" title=\"What is Dot Product?\">What is Dot 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\/dot-product\/#Concept_of_Dot_Product\" title=\"Concept of Dot Product\">Concept of Dot 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\/dot-product\/#Dot_Product_-_Geometrical_Definition\" title=\"Dot Product &#8211; Geometrical Definition\">Dot Product &#8211; Geometrical Definition<\/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\/dot-product\/#Dot_Product_-_Algebraic_Definition\" title=\"Dot Product &#8211; Algebraic Definition\">Dot Product &#8211; Algebraic Definition<\/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\/dot-product\/#Properties_of_Dot_Product\" title=\"Properties of Dot Product\">Properties of Dot Product<\/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\/dot-product\/#The_Formula_for_Dot_Product\" title=\"The Formula for Dot Product\">The Formula for Dot Product<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Dot_Product\"><\/span>What is Dot Product?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The dot product is a mathematical operation that takes two vectors and returns a single number. The number is the product of the lengths of the vectors multiplied by the cosine of the angle between them.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153801 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/dot-product-geometric-definition-concept-algebraic-definition-properties-formula-solved-examples-and-faqs.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/dot-product-geometric-definition-concept-algebraic-definition-properties-formula-solved-examples-and-faqs.jpg?v=1648228778 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/dot-product-geometric-definition-concept-algebraic-definition-properties-formula-solved-examples-and-faqs-300x212.jpg?v=1648228778 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Concept_of_Dot_Product\"><\/span>Concept of Dot Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Dot Product is a mathematical operation that takes two vectors and calculates the product of their lengths (magnitudes) and the cosine of the angle between them. The Dot Product is written as:<\/p>\n<p>\\begin{align}<\/p>\n<p>\\mathbf{A} \\cdot \\mathbf{B}<\/p>\n<p>\\end{align}<\/p>\n<p>where \\mathbf{A} and \\mathbf{B} are vectors.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Dot_Product_-_Geometrical_Definition\"><\/span>Dot Product &#8211; Geometrical Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Dot Product is a mathematical operation that takes two vectors as input and produces a scalar result. The Dot Product is denoted by the symbol &#8220;\u00b7&#8221; and is defined as follows:<\/p>\n<p>The Dot Product is a measure of the similarity of two vectors. The Dot Product is zero if and only if the vectors are perpendicular to each other. If the vectors are not perpendicular to each other, then the Dot Product is non-zero and is proportional to the cosine of the angle between the vectors.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Dot_Product_-_Algebraic_Definition\"><\/span>Dot Product &#8211; Algebraic Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The dot product of two vectors is a scalar value that is the product of the lengths of the vectors multiplied by the cosine of the angle between them.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Dot_Product\"><\/span>Properties of Dot Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The dot product is a vector quantity and has the following properties:<\/p>\n<p>The dot product is commutative.<\/p>\n<p>The dot product is distributive.<\/p>\n<p>The dot product is associative.<\/p>\n<p>The dot product is symmetric.<\/p>\n<p>The dot product is positive definite.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Formula_for_Dot_Product\"><\/span>The Formula for Dot Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The dot product is a mathematical operation that takes two vectors and calculates the product of their lengths times the cosine of the angle between them.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Dot Product? The dot product is a mathematical operation that takes two vectors and returns a single number. [&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":"Dot Product - Geometric Definition, Concept, Algebraic Definition, Properties, Formula, Solved Examples, and FAQs","_yoast_wpseo_title":"Dot Product - Geometric Definition, Concept, Algebraic Definition?","_yoast_wpseo_metadesc":"Learn about dot product topic of maths in details explained by subject experts on infinitylearn.com. 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