{"id":435,"date":"2015-06-16T12:40:40","date_gmt":"2015-06-16T10:40:40","guid":{"rendered":"http:\/\/wpcalc.com\/?p=435"},"modified":"2025-05-09T08:03:35","modified_gmt":"2025-05-09T05:03:35","slug":"3d-vector-scalar-product","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/3d-vector-scalar-product\/","title":{"rendered":"3D Vector Scalar Product Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 class=\"text-lg font-display font-bold\">3D Vector Scalar Product Calculator Calculator<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"435\" data-favorite-title=\"3D Vector Scalar Product\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/3d-vector-scalar-product\/\" data-favorite-excerpt=\"The 3D Vector Scalar Product calculator helps you find the dot product (scalar product) of two three-dimensional vectors. It\u2019s useful in physics, engineering, and computer graphics to measure how much two vectors align or to find the angle between them. Just input the components of both vectors and get the scalar result instantly.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/mathematics\/3d-vector-scalar-product\/\" method=\"POST\" class=\"calculator\" id=\"calculator-435\" data-post=\"435\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Vector V1 - X<\/label><input type=\"number\" name=\"vector_v1_x\" id=\"field-1\" placeholder=\"1\" step=\"1\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Vector V1 - Y<\/label><input type=\"number\" name=\"vector_v1_y\" id=\"field-2\" placeholder=\"2\" step=\"1\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Vector V1 - Z<\/label><input type=\"number\" name=\"vector_v1_z\" id=\"field-3\" placeholder=\"3\" step=\"1\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">Vector V2 - X<\/label><input type=\"number\" name=\"vector_v2_x\" id=\"field-4\" placeholder=\"4\" step=\"1\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-5\">Vector V2 - Y<\/label><input type=\"number\" name=\"vector_v2_y\" id=\"field-5\" placeholder=\"5\" step=\"1\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">Vector V2 - Z<\/label><input type=\"number\" name=\"vector_v2_z\" id=\"field-6\" placeholder=\"6\" step=\"1\" value=\"6\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"435\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Scalar Product<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"435\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Dot Product Formula for 3D Vectors<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">$$\\vec{A} \\cdot \\vec{B} = A_x B_x + A_y B_y + A_z B_z$$<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p>Where:<\/p>\n<ul>\n<li>$$\\vec{A} = (A_x, A_y, A_z)$$<\/li>\n<li>$$\\vec{B} = (B_x, B_y, B_z)$$<\/li>\n<li>The result is a <strong>scalar<\/strong>, not a vector.<\/li>\n<\/ul>\n<p>This formula multiplies corresponding components of the vectors and sums them up.<br \/>\r\n<\/section>\n<p>The scalar (dot) product is a fundamental operation in vector mathematics. It\u2019s often used to determine the angle between two vectors, to check orthogonality (if the result is 0), or to project one vector onto another. For example, in 3D graphics, it\u2019s essential for lighting calculations and camera orientation. Simply input the x, y, and z components of both vectors, and the calculator will return the scalar result.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The 3D Vector Scalar Product calculator helps you find the dot product (scalar product) of two three-dimensional vectors. It\u2019s useful in physics, engineering, and computer graphics to measure how much two vectors align or to find the angle between them. Just input the components of both vectors and get the scalar result instantly.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[23],"class_list":["post-435","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-geometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/435","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=435"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/435\/revisions"}],"predecessor-version":[{"id":63864,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/435\/revisions\/63864"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=435"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=435"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=435"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}