{"id":94199,"date":"2025-01-23T06:43:38","date_gmt":"2025-01-23T03:13:38","guid":{"rendered":"https:\/\/nabfollower.com\/blog\/multiplying-vectors-by-a-scalar-l5p\/"},"modified":"2025-01-23T06:43:38","modified_gmt":"2025-01-23T03:13:38","slug":"multiplying-vectors-by-a-scalar-l5p","status":"publish","type":"post","link":"https:\/\/nabfollower.com\/blog\/multiplying-vectors-by-a-scalar-l5p\/","title":{"rendered":"\u0636\u0631\u0628 \u0628\u0631\u062f\u0627\u0631\u0647\u0627 \u062f\u0631 \u0627\u0633\u06a9\u0627\u0644\u0631"},"content":{"rendered":"<div data-article-id=\"2234600\" id=\"article-body\">\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter-rtl ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628<\/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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/nabfollower.com\/blog\/multiplying-vectors-by-a-scalar-l5p\/#%D9%85%D9%81%D9%87%D9%88%D9%85_%DA%A9%D9%84%DB%8C%D8%AF%DB%8C\" >\u0645\u0641\u0647\u0648\u0645 \u06a9\u0644\u06cc\u062f\u06cc:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/nabfollower.com\/blog\/multiplying-vectors-by-a-scalar-l5p\/#%D9%85%D8%AB%D8%A7%D9%84_1_%D8%B6%D8%B1%D8%A8_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1_a21_%D8%AA%D9%88%D8%B3%D8%B7_%D8%A7%D8%B3%DA%A9%D8%A7%D9%84%D8%B1_3\" >\u0645\u062b\u0627\u0644 1: \u0636\u0631\u0628 \u0628\u0631\u062f\u0627\u0631 a=[2,1] \u062a\u0648\u0633\u0637 \u0627\u0633\u06a9\u0627\u0644\u0631 3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/nabfollower.com\/blog\/multiplying-vectors-by-a-scalar-l5p\/#%D9%85%D8%AB%D8%A7%D9%84_2_%D8%B6%D8%B1%D8%A8_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1_a21_%D8%AA%D9%88%D8%B3%D8%B7_Scalar_-1\" >\u0645\u062b\u0627\u0644 2: \u0636\u0631\u0628 \u0628\u0631\u062f\u0627\u0631 a=[2,1] \u062a\u0648\u0633\u0637 Scalar -1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/nabfollower.com\/blog\/multiplying-vectors-by-a-scalar-l5p\/#%D9%85%D8%B4%D8%A7%D9%87%D8%AF%D8%A7%D8%AA\" >\u0645\u0634\u0627\u0647\u062f\u0627\u062a:<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%D9%85%D9%81%D9%87%D9%88%D9%85_%DA%A9%D9%84%DB%8C%D8%AF%DB%8C\"><\/span>\n<p>  \u0645\u0641\u0647\u0648\u0645 \u06a9\u0644\u06cc\u062f\u06cc:<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0636\u0631\u0628 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u06cc\u06a9 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u0622\u0646 \u0627\u0633\u06a9\u0627\u0644\u0631 \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u062c\u0647\u062a \u0622\u0646 \u0631\u0627 \u062d\u0641\u0638 \u0645\u06cc \u06a9\u0646\u062f (\u06cc\u0627 \u0645\u0639\u06a9\u0648\u0633 \u06a9\u0631\u062f\u0646 \u0622\u0646 \u062f\u0631 \u0635\u0648\u0631\u062a \u0645\u0646\u0641\u06cc \u0628\u0648\u062f\u0646 \u0627\u0633\u06a9\u0627\u0644\u0631) \u0627\u0633\u062a.<br \/>\u0627\u06af\u0631 <strong>\u0627\u0644\u0641<\/strong> \u0628\u0631\u062f\u0627\u0631 \u0627\u0633\u062a \u0648 <strong>\u06a9<\/strong> \u06cc\u06a9 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0627\u0633\u062a\u060c \u0646\u062a\u06cc\u062c\u0647 \u0622\u0646 \u0627\u0633\u062a<\/p>\n<ul>\n<li>a\u22c5k=[a1.k,a2\u22c5k]\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 a1 \u0648 a2 \u0627\u062c\u0632\u0627\u06cc \u0628\u0631\u062f\u0627\u0631 \u0647\u0633\u062a\u0646\u062f.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"%D9%85%D8%AB%D8%A7%D9%84_1_%D8%B6%D8%B1%D8%A8_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1_a21_%D8%AA%D9%88%D8%B3%D8%B7_%D8%A7%D8%B3%DA%A9%D8%A7%D9%84%D8%B1_3\"><\/span>\n<p>  \u0645\u062b\u0627\u0644 1: \u0636\u0631\u0628 \u0628\u0631\u062f\u0627\u0631 a=[2,1] \u062a\u0648\u0633\u0637 \u0627\u0633\u06a9\u0627\u0644\u0631 3<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. \u0628\u0631\u062f\u0627\u0631 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647:<\/strong> <strong><em>\u0627\u0644\u0641<\/em><\/strong>=[2,1]\n<p><strong>2. \u0627\u0633\u06a9\u0627\u0644\u0631:<\/strong> <strong><em>\u06a9<\/em><\/strong>=3<\/p>\n<p><strong>3. \u0645\u062d\u0627\u0633\u0628\u0647:<\/strong> <strong><em>\u0627\u0644\u0641<\/em><\/strong>\u22c5<strong>3<\/strong>= [2\u22c53,1\u22c53] = [6,3]\n<p><strong>4. \u0646\u062a\u06cc\u062c\u0647:<\/strong> [6,3]\n<p><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D9%85%D8%AB%D8%A7%D9%84_2_%D8%B6%D8%B1%D8%A8_%D8%A8%D8%B1%D8%AF%D8%A7%D8%B1_a21_%D8%AA%D9%88%D8%B3%D8%B7_Scalar_-1\"><\/span>\n<p>  \u0645\u062b\u0627\u0644 2: \u0636\u0631\u0628 \u0628\u0631\u062f\u0627\u0631 a=[2,1] \u062a\u0648\u0633\u0637 Scalar -1<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. \u0628\u0631\u062f\u0627\u0631 \u062f\u0627\u062f\u0647 \u0634\u062f\u0647:<\/strong> <strong><em>\u0627\u0644\u0641<\/em><\/strong>=[2,1]\n<p><strong>2. \u0627\u0633\u06a9\u0627\u0644\u0631:<\/strong> <strong><em>\u06a9<\/em><\/strong>=-1<\/p>\n<p><strong>3. \u0645\u062d\u0627\u0633\u0628\u0647:<\/strong> <strong><em>\u0627\u0644\u0641<\/em><\/strong>\u22c5<strong>-1<\/strong>= [2\u22c5-1,1\u22c5-1] = [-2,-1]\n<p><strong>4. \u0646\u062a\u06cc\u062c\u0647:<\/strong> [-2,-1]\n<p><img decoding=\"async\" src=\"https:\/\/media2.dev.to\/dynamic\/image\/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto\/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F5dcnnkulevzg9z92g5sg.png\" alt=\"\u0645\u062b\u0627\u0644-2\" loading=\"lazy\" width=\"800\" height=\"449\" title=\"\"><\/p>\n<h2><span class=\"ez-toc-section\" id=\"%D9%85%D8%B4%D8%A7%D9%87%D8%AF%D8%A7%D8%AA\"><\/span>\n<p>  \u0645\u0634\u0627\u0647\u062f\u0627\u062a:<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>\u0648\u0642\u062a\u06cc \u062f\u0631 3 \u0636\u0631\u0628 \u0645\u06cc \u0634\u0648\u062f\u060c \u0642\u062f\u0631 \u0628\u0631\u062f\u0627\u0631 \u0633\u0647 \u0628\u0631\u0627\u0628\u0631 \u0645\u06cc \u0634\u0648\u062f \u0648 \u062c\u0647\u062a \u062b\u0627\u0628\u062a \u0645\u06cc \u0645\u0627\u0646\u062f.<\/li>\n<li>\u0648\u0642\u062a\u06cc \u062f\u0631 1- \u0636\u0631\u0628 \u0645\u06cc \u0634\u0648\u062f\u060c \u0642\u062f\u0631 \u0628\u0631\u062f\u0627\u0631 \u062b\u0627\u0628\u062a \u0645\u06cc \u0645\u0627\u0646\u062f\u060c \u0627\u0645\u0627 \u062c\u0647\u062a \u0645\u0639\u06a9\u0648\u0633 \u0645\u06cc \u0634\u0648\u062f.<\/li>\n<\/ul><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0641\u0647\u0648\u0645 \u06a9\u0644\u06cc\u062f\u06cc: \u0636\u0631\u0628 \u06cc\u06a9 \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u06cc\u06a9 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0627\u0646\u062f\u0627\u0632\u0647 \u0628\u0631\u062f\u0627\u0631 \u062f\u0631 \u0622\u0646 \u0627\u0633\u06a9\u0627\u0644\u0631 \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u062c\u0647\u062a \u0622\u0646 \u0631\u0627 \u062d\u0641\u0638 \u0645\u06cc \u06a9\u0646\u062f (\u06cc\u0627 \u0645\u0639\u06a9\u0648\u0633 \u06a9\u0631\u062f\u0646 \u0622\u0646 \u062f\u0631 \u0635\u0648\u0631\u062a \u0645\u0646\u0641\u06cc \u0628\u0648\u062f\u0646 \u0627\u0633\u06a9\u0627\u0644\u0631) \u0627\u0633\u062a.\u0627\u06af\u0631 \u0627\u0644\u0641 \u0628\u0631\u062f\u0627\u0631 \u0627\u0633\u062a \u0648 \u06a9 \u06cc\u06a9 \u0627\u0633\u06a9\u0627\u0644\u0631 \u0627\u0633\u062a\u060c \u0646\u062a\u06cc\u062c\u0647 \u0622\u0646 \u0627\u0633\u062a a\u22c5k=[a1.k,a2\u22c5k]\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 a1 \u0648 a2 &hellip;<\/p>\n","protected":false},"author":2,"featured_media":94200,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","footnotes":""},"categories":[339],"tags":[],"class_list":["post-94199","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dev"],"_links":{"self":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/94199","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/comments?post=94199"}],"version-history":[{"count":0,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/94199\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media\/94200"}],"wp:attachment":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media?parent=94199"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/categories?post=94199"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/tags?post=94199"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}