{"id":155002,"date":"2022-03-26T00:09:41","date_gmt":"2022-03-25T18:39:41","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/scalar-triple-product-formula-proof-properties-and-faqs\/"},"modified":"2024-05-06T15:00:09","modified_gmt":"2024-05-06T09:30:09","slug":"scalar-triple-product-formula-proof-properties-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/scalar-triple-product\/","title":{"rendered":"Scalar Triple Product"},"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\/scalar-triple-product\/#Scalar_Triple_Product_Formula\" title=\"Scalar Triple Product Formula\">Scalar Triple Product Formula<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/scalar-triple-product\/#A_Proof_of_Scalar_Triple_Products\" title=\"A Proof of Scalar Triple Products\">A Proof of Scalar Triple Products<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/scalar-triple-product\/#From_the_properties_of_the_dot_product_of_vectors\" title=\"From the properties of the dot product of vectors\">From the properties of the dot product of vectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/scalar-triple-product\/#Scalar_Triple_Product_Properties\" title=\"Scalar Triple Product Properties\">Scalar Triple Product Properties<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/scalar-triple-product\/#Analysing_the_scalar_triple_product_formula_some_can_drawn\" title=\"Analysing the scalar triple product formula, some can drawn:\">Analysing the scalar triple product formula, some can drawn:<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Scalar_Triple_Product_Formula\"><\/span>Scalar Triple Product Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Scalar Triple Product \u2013 Formula: The scalar triple product is a mathematical formula that calculates the volume of a parallelepiped, which is a three-dimensional object with six faces. The formula uses the dot product, which is a mathematical formula that calculates the length of a vector, and the cross product, which is a mathematical formula that calculates the vector perpendicular to two other vectors.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"A_Proof_of_Scalar_Triple_Products\"><\/span>A Proof of Scalar Triple Products<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A proof of the scalar triple product is a mathematical proof that shows that the scalar triple product is a real number. The proof begins by showing that the scalar triple product is associative. The proof then shows that the scalar triple product is distributive. Finally, the proof shows that the scalar triple product is commutative.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"From_the_properties_of_the_dot_product_of_vectors\"><\/span>From the properties of the dot product of vectors<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The dot product of two vectors is a measure of how closely the two vectors are aligned. The dot product is also a measure of the magnitude of the two vectors, and the direction of the two vectors.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Scalar_Triple_Product_Properties\"><\/span>Scalar Triple Product Properties<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The scalar triple product is distributive over addition and scalar multiplication.<\/p>\n<p>(A \u00b7 B) \u00b7 C = A \u00b7 (B \u00b7 C)<\/p>\n<p>A \u00b7 (B + C) = A \u00b7 B + A \u00b7 C<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Analysing_the_scalar_triple_product_formula_some_can_drawn\"><\/span>Analysing the scalar triple product formula, some can drawn:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A vector has magnitude and direction. Magnitude measured in terms of length and direction is measured in terms of angles. For two vectors, the magnitude is the sum of the lengths of the vectors and the direction is the angle between the vectors.<\/p>\n<p>The magnitude of a vector is always positive. The direction of a vector can be either positive or negative, depending on the angle between the vectors.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Scalar Triple Product Formula Scalar Triple Product \u2013 Formula: The scalar triple product is a mathematical formula that calculates the [&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":"Scalar Triple Product","_yoast_wpseo_title":"Scalar Triple Product \u2013 Formula, Proof, Properties and FAQs","_yoast_wpseo_metadesc":"Learn about scalar triple product topic of maths in details explained by subject experts on infinitylearn.com. 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