{"id":431,"date":"2015-06-16T12:15:40","date_gmt":"2015-06-16T10:15:40","guid":{"rendered":"http:\/\/wpcalc.com\/?p=431"},"modified":"2025-05-09T08:04:57","modified_gmt":"2025-05-09T05:04:57","slug":"2d-vector-scalar-product","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/2d-vector-scalar-product\/","title":{"rendered":"2D 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\">Calculate the Dot Product of Two 2D Vectors<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"431\" data-favorite-title=\"2D Vector Scalar Product \" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/2d-vector-scalar-product\/\" data-favorite-excerpt=\"The 2D Vector Scalar Product Calculator helps you compute the scalar (dot) product of two 2D vectors. This tool is useful for students, engineers, and anyone working with vector mathematics. It takes the x and y components of each vector and returns a single number representing their scalar product, which can indicate the angle relationship between them.\" 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\/2d-vector-scalar-product\/\" method=\"POST\" class=\"calculator\" id=\"calculator-431\" data-post=\"431\"><fieldset class=\"fieldset-input\"><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=\"2\" step=\"1\" value=\"2\"\/><\/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=\"3\" step=\"1\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Vector V2 - X<\/label><input type=\"number\" name=\"vector_v2_x\" id=\"field-3\" placeholder=\"4\" step=\"1\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">Vector V2 - Y<\/label><input type=\"number\" name=\"vector_v2_y\" id=\"field-4\" placeholder=\"5\" step=\"1\" value=\"5\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"431\">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=\"431\" 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 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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 2D 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 \\cdot B_x + A_y \\cdot B_y \\)<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$A_x, A_y$$ \u2014 components of vector A<\/li>\n<li>\\(B_x, B_y\\) \u2014 components of vector B<\/li>\n<\/ul>\n<p>This formula calculates the scalar product by multiplying the corresponding components of two vectors and summing the results.<br \/>\r\n<\/section>\n<p>The scalar (dot) product of two 2D vectors measures how much one vector extends in the direction of another. It is commonly used in physics, computer graphics, and engineering to determine angles between vectors, check for orthogonality (dot product = 0), or project one vector onto another. <\/p>\n<p><strong>For example<\/strong>, if \\(\\vec{A} = (2, 3)\\) and \\(\\vec{B} = (4, -1)\\), the dot product is \\(2 \\cdot 4 + 3 \\cdot (-1)\\) = 8 &#8211; 3 = 5. A positive result indicates an acute angle between vectors, zero means they are perpendicular, and negative indicates an obtuse angle.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The 2D Vector Scalar Product Calculator helps you compute the scalar (dot) product of two 2D vectors. This tool is useful for students, engineers, and anyone working with vector mathematics. It takes the x and y components of each vector and returns a single number representing their scalar product, which can indicate the angle relationship between them.<\/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-431","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\/431","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=431"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/431\/revisions"}],"predecessor-version":[{"id":63868,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/431\/revisions\/63868"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}