{"id":156442,"date":"2022-03-26T01:45:42","date_gmt":"2022-03-25T20:15:42","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/cross-product-formula-properties-and-calculating-cross-product\/"},"modified":"2022-12-22T21:39:06","modified_gmt":"2022-12-22T16:09:06","slug":"cross-product-formula-properties-and-calculating-cross-product","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/cross-product\/","title":{"rendered":"Cross Product \u2013 Formula, Properties and Calculating Cross 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\/cross-product\/#What_is_Cross_Product\" title=\"What is Cross Product?\">What is Cross 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\/cross-product\/#The_Cross-multiplication_Formula\" title=\"The Cross-multiplication Formula\">The Cross-multiplication Formula<\/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\/cross-product\/#Properties_of_Cross_Product\" title=\"Properties of Cross Product\">Properties of Cross 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\/cross-product\/#Calculating_Cross_Product\" title=\"Calculating Cross Product\">Calculating Cross Product<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Cross_Product\"><\/span>What is Cross Product?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cross_product\">cross product<\/a> is a vector operator that takes two vectors as input and produces a third vector as output. The cross product is defined as the vector product of two vectors, and is denoted by the symbol . Cross product is perpendicular to both input vectors, and its magnitude is equal to the product of the magnitudes of the input vectors multiplied by the sine of the angle between them. Cross Product \u2013 Formula.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156441 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/cross-product-formula-properties-and-calculating-cross-product.jpg\" alt=\"Cross Product \u2013 Formula, Properties and Calculating Cross Product\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/cross-product-formula-properties-and-calculating-cross-product.jpg?v=1648239338 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/cross-product-formula-properties-and-calculating-cross-product-300x212.jpg?v=1648239338 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Cross-multiplication_Formula\"><\/span>The Cross-multiplication Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The cross-multiplication formula is used to solve systems of linear equations. The formula is as follows:<\/p>\n<p>$\\left(\\begin{array}{c}a\\\\b\\\\c\\\\d\\\\e\\\\f\\\\g\\\\h\\end{array}\\right)=\\left(\\begin{array}{c}x\\\\y\\\\z\\\\w\\\\x\\\\y\\\\z\\\\w\\end{array}\\right)$<\/p>\n<p>In the formula, $a$, $b$, $c$, $d$, $e$, $f$, and $g$ are the coefficients of the first equation, and $h$ is the coefficient of the second equation. $x$, $y$, $z$, and $w$ are the variables in the equation.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Properties_of_Cross_Product\"><\/span>Properties of Cross Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The following are some of the most important properties of the cross product:<\/p>\n<p>1. The cross product is perpendicular to both of the vectors that are involved in the product.<\/p>\n<p>2. The magnitude of the cross product is the product of the magnitudes of the two vectors, and the direction of the cross product is determined by the right hand rule.<\/p>\n<p>3. The cross product is a vector quantity.<\/p>\n<p>4. The cross product is associative &#8211; that is, the order of the vectors that are involved in the product does not affect the result.<\/p>\n<p>5. The cross product is commutative &#8211; that is, the order of the vectors that are involved in the product does not affect the result.<\/p>\n<p>6. The cross product is distributive &#8211; that is, the product of a vector and a scalar is the same as the vector cross product of the vector and the scalar.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Calculating_Cross_Product\"><\/span>Calculating Cross Product<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To calculate a cross product, first identify the two vectors that you want to multiply. Next, use the following formula:<\/p>\n<p>(A x B) = A.B sin\u03b8<\/p>\n<p>In this equation, A is the first vector, B is the second vector, and \u03b8 is the angle between the two vectors.<\/p>\n<p>Cross Product \u2013 Formula.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is Cross Product? The cross product is a vector operator that takes two vectors as input and produces a [&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":"Cross Product \u2013 Formula","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Cross Product \u2013 Formula topic of maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/cross-product\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Cross Product \u2013 Formula, Properties and Calculating Cross Product - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Cross Product \u2013 Formula topic of maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/cross-product\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cross Product \u2013 Formula, Properties and Calculating Cross Product - 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