{"id":74,"date":"2023-09-16T13:03:21","date_gmt":"2023-09-16T13:03:21","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b5-%d0%b4%d0%b2%d1%83%d1%85-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be\/"},"modified":"2023-09-16T13:03:21","modified_gmt":"2023-09-16T13:03:21","slug":"%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b5-%d0%b4%d0%b2%d1%83%d1%85-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b5-%d0%b4%d0%b2%d1%83%d1%85-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be\/","title":{"rendered":"\u041f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435)"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0438 \u043a\u0430\u043a \u043e\u043d\u043e \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0432\u0438\u0434\u0438\u0442\u0435, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 (\u0438\u043b\u0438 \u0448\u0442\u043e\u043f\u043e\u0440). \u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-producto-vectorial-de-dos-vectores\"><\/span> \u0427\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0412 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 <strong>\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/strong> \u2014 \u044d\u0442\u043e \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u0432 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0432 R3). \u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u044d\u0442\u043e\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0439 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0432\u0435\u043a\u0442\u043e\u0440 \u0441 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b\u043c \u0434\u0432\u0443\u043c \u043f\u0435\u0440\u0435\u043c\u043d\u043e\u0436\u0435\u043d\u043d\u044b\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c, \u0438 \u0441 \u043c\u043e\u0434\u0443\u043b\u0435\u043c, \u0440\u0430\u0432\u043d\u044b\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044e \u043c\u043e\u0434\u0443\u043b\u0435\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432-\u043c\u043d\u043e\u0436\u0438\u0442\u0435\u043b\u0435\u0439 \u043d\u0430 \u0441\u0438\u043d\u0443\u0441 \u043e\u0431\u0440\u0430\u0437\u0443\u0435\u043c\u043e\u0433\u043e \u0438\u043c\u0438 \u0443\u0433\u043b\u0430. \u0414\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u0442\u0430\u043a\u043e\u0432\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-625267c9d98347748a771c7cec9bfcec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert = \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}}\\rvert \\cdot \\text{sen}(\\alpha)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u0432\u044b \u0432\u0438\u0434\u0438\u0442\u0435 \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435, \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-850177c0489097bd9409ba9b13b07506_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{\\times}\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> , \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0433\u043e \u0435\u0449\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 <strong>\u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u044b\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c.<\/strong> \u0415\u0433\u043e \u0442\u0430\u043a\u0436\u0435 \u0438\u043d\u043e\u0433\u0434\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u044e\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c \u0413\u0438\u0431\u0431\u0441\u0430, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d \u0435\u0433\u043e \u0438\u0437\u043e\u0431\u0440\u0435\u043b. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/quel-est-le-produit-vectoriel-de-deux-vecteurs-.webp\" alt=\"\" class=\"wp-image-3883\" width=\"307\" height=\"310\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> \u041a\u0430\u043a \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0432\u0438\u0434\u0435\u0442\u044c \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0433\u0440\u0430\u0444\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0438\u0438, \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e \u0434\u0432\u0443\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c, \u043d\u0430 \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043d\u0438 \u043f\u0435\u0440\u0435\u043c\u043d\u043e\u0436\u0430\u044e\u0442\u0441\u044f, \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u043d\u043e \u043d\u043e\u0440\u043c\u0430\u043b\u044c\u043d\u043e \u043a \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0438\u0445 \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-para-calcular-el-producto-vectorial-de-dos-vectores\"><\/span> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0415\u0441\u043b\u0438 \u043c\u044b \u0437\u043d\u0430\u0435\u043c \u0434\u0435\u043a\u0430\u0440\u0442\u043e\u0432\u044b \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0441\u0430\u043c\u044b\u0439 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0441\u043f\u043e\u0441\u043e\u0431 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u2014 \u043d\u0430\u0439\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c 3&#215;3. \u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435, \u043a\u0430\u043a \u044d\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442\u0441\u044f: <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043b\u044e\u0431\u044b\u0435 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-581394386a4c68ca2bfa92fb4e2445ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (\\text{u}_x,\\text{u}_y,\\text{u}_z) \\qquad \\vv{\\text{v}}= (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"267\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u0415\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56551111a4f5a18a4609772ebaeaf919_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] \\text{u}_x &amp; \\text{u}_y &amp; \\text{u}_z \\\\[1.1ex] \\text{v}_x &amp;\\text{v}_y&amp;\\text{v}_z \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u0413\u0434\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-899f7cb82c85508ac2129e2393976f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{i}, \\vv{j},\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"38\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u042d\u0442\u043e \u0435\u0434\u0438\u043d\u0438\u0447\u043d\u044b\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0432 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f\u0445 \u043e\u0441\u0435\u0439 X, Y \u0438 Z \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e.<\/p>\n<\/div>\n<p> \u0414\u0430\u0432\u0430\u0439\u0442\u0435 \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-89a657062237b32001dad723a07ad2ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (3,1,0) \\qquad \\vv{\\text{v}}= (2,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"227\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0427\u0442\u043e\u0431\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0442\u0440\u0435\u0442\u044c\u0435\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-abc77b698bf6f4fddec1ab2dcc8b07f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; 1 &amp; 0 \\\\[1.1ex] 2 &amp;1&amp;-1 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"145\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0431\u0443\u0434\u0435\u043c \u0440\u0435\u0448\u0430\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u0434\u044a\u044e\u0432\u0430\u043d\u0442\u043e\u0432 \u0438\u043b\u0438 \u043a\u043e\u0444\u0430\u043a\u0442\u043e\u0440\u043e\u0432 (\u043c\u043e\u0436\u043d\u043e \u0442\u0430\u043a\u0436\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0421\u0430\u0440\u0440\u044e\u0441\u0430):<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-eeeac04b3f0edd64e5413629051551fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; 1 &amp; 0 \\\\[1.1ex] 2 &amp;1&amp;-1 \\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} 1 &amp; 0 \\\\[1.1ex] 1&amp;-1 \\end{vmatrix} -\\vv{j}\\begin{vmatrix}  3&amp;  0 \\\\[1.1ex] 2 &amp;-1 \\end{vmatrix}+\\vv{z}\\begin{vmatrix}3&amp; 1 \\\\[1.1ex] 2 &amp;1 \\end{vmatrix}  \\\\[2ex] &amp; = -\\vv{i}+3\\vv{j}+\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"411\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0431\u0443\u0434\u0435\u0442: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-625f3af33d3cd3b9991682014c911024_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\bm{(-1,3,1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-la-direccion-y-el-sentido-del-producto-vectorial\"><\/span> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0418\u043d\u043e\u0433\u0434\u0430 \u043d\u0430\u043c \u043d\u0435 \u043d\u0443\u0436\u043d\u043e \u0437\u043d\u0430\u0442\u044c \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u043d\u043e \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044c, \u0435\u0433\u043e \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435. \u0422\u0430\u043a\u043e\u0435 \u0447\u0430\u0441\u0442\u043e \u0441\u043b\u0443\u0447\u0430\u0435\u0442\u0441\u044f \u0432 \u0444\u0438\u0437\u0438\u043a\u0435, \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e \u043f\u0440\u0438 \u0440\u0430\u0441\u0447\u0435\u0442\u0435 \u0441\u0438\u043b.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u043f\u0440\u0430\u0432\u0438\u043b \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u044f \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u043c\u0438 \u0438\u0437 \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f <strong>\u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438<\/strong> , \u043b\u0438\u0431\u043e \u0442\u0440\u0435\u043c\u044f \u043f\u0430\u043b\u044c\u0446\u0430\u043c\u0438, \u043b\u0438\u0431\u043e \u0432\u0441\u0435\u0439 \u0440\u0443\u043a\u043e\u0439, \u0438 <strong>\u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0448\u0442\u043e\u043f\u043e\u0440\u0430 (\u0438\u043b\u0438 \u0432\u0438\u043d\u0442\u0430)<\/strong> . \u0412\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043b\u044e\u0431\u043e\u0435 \u0438\u0437 \u043d\u0438\u0445, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0432\u0430\u043c \u043d\u0435 \u043e\u0431\u044f\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u0437\u043d\u0430\u0442\u044c \u0438\u0445 \u0432\u0441\u0435, \u043c\u044b \u0432\u0441\u0435 \u0440\u0430\u0432\u043d\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u0438\u043c \u0432\u0430\u043c \u0442\u0440\u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u0430, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u043f\u0440\u0438\u0434\u0435\u0440\u0436\u0438\u0432\u0430\u0442\u044c\u0441\u044f \u0442\u043e\u0433\u043e, \u043a\u043e\u0442\u043e\u0440\u043e\u0435 \u0432\u0430\u043c \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0440\u0430\u0432\u0438\u0442\u0441\u044f. \ud83d\ude09<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-mano-derecha-3-dedos\"><\/span> \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 (3 \u043f\u0430\u043b\u044c\u0446\u0430)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0412\u0435\u0440\u0441\u0438\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0438\u043b\u0438 \u0437\u0430\u043a\u043e\u043d\u0430 \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 \u0441 \u0442\u0440\u0435\u043c\u044f \u043f\u0430\u043b\u044c\u0446\u0430\u043c\u0438 \u043f\u0440\u0435\u0434\u043f\u043e\u043b\u0430\u0433\u0430\u0435\u0442 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0448\u0430\u0433\u043e\u0432:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u041f\u043e\u043c\u0435\u0441\u0442\u0438\u0442\u0435 \u0443\u043a\u0430\u0437\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0439 \u043f\u0430\u043b\u0435\u0446 \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 \u043a \u043f\u0435\u0440\u0432\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a13b5c3a9f833efc0ddf4caf790f0483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">\u041f\u043e\u043c\u0435\u0441\u0442\u0438\u0442\u0435 \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043f\u0430\u043b\u0435\u0446 (\u0438\u043b\u0438 \u0441\u0440\u0435\u0434\u043d\u0438\u0439 \u043f\u0430\u043b\u0435\u0446) \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 \u043a\u043e \u0432\u0442\u043e\u0440\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acab6198e5d0337e7d0e9ed7814c16d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u043e\u0433\u043e \u043f\u0430\u043b\u044c\u0446\u0430 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fce88450a631ec24e37f45befae0675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}\\times\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> <\/li>\n<\/ol>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/regle-ou-loi-de-la-main-droite.webp\" alt=\"\" class=\"wp-image-892\" width=\"392\" height=\"353\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-de-la-mano-derecha-palma-de-la-mano\"><\/span> \u041f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 (\u043b\u0430\u0434\u043e\u043d\u044c)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u041b\u0430\u0434\u043e\u043d\u043d\u0430\u044f \u0432\u0435\u0440\u0441\u0438\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u0430 \u0438\u043b\u0438 \u0437\u0430\u043a\u043e\u043d\u0430 \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 \u043e\u0447\u0435\u043d\u044c \u043f\u043e\u0445\u043e\u0436\u0430 \u043d\u0430 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u0435 \u043f\u0440\u0430\u0432\u0438\u043b\u043e. \u0427\u0442\u043e\u0431\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0442\u044c \u0435\u0433\u043e, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u043f\u043e\u043b\u043d\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0448\u0430\u0433\u0438:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u041f\u043e\u043c\u0435\u0441\u0442\u0438\u0442\u0435 \u043f\u0440\u0430\u0432\u0443\u044e \u0440\u0443\u043a\u0443 \u043f\u0430\u043b\u044c\u0446\u0430\u043c\u0438 \u0432 \u0442\u043e\u043c \u0436\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438, \u0447\u0442\u043e \u0438 \u043f\u0435\u0440\u0432\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a13b5c3a9f833efc0ddf4caf790f0483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">\u0417\u0430\u043a\u0440\u043e\u0439\u0442\u0435 \u043f\u0440\u0430\u0432\u0443\u044e \u0440\u0443\u043a\u0443, \u043f\u0435\u0440\u0435\u043c\u0435\u0441\u0442\u0438\u0432 \u043f\u0430\u043b\u044c\u0446\u044b \u043a\u043e \u0432\u0442\u043e\u0440\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acab6198e5d0337e7d0e9ed7814c16d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"26\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> \u0421\u043e\u043c\u043a\u043d\u0443\u0442\u044c \u0440\u0443\u043a\u0443 \u043d\u0443\u0436\u043d\u043e \u0441 \u0442\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0433\u0434\u0435 \u0443\u0433\u043e\u043b (\u0438\u043b\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435) \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u043c\u0435\u043d\u044c\u0448\u0435.<\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">\u041f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0435 \u043f\u043e\u043b\u043e\u0436\u0435\u043d\u0438\u0435 \u0431\u043e\u043b\u044c\u0448\u043e\u0433\u043e \u043f\u0430\u043b\u044c\u0446\u0430 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fce88450a631ec24e37f45befae0675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}\\times\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> <\/li>\n<\/ol>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/vecteur-produit-regle-de-droite.webp\" alt=\"\u043f\u0440\u0430\u0432\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043a\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\" class=\"wp-image-898\" width=\"373\" height=\"342\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"regla-del-sacacorchos\"><\/span> \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0448\u0442\u043e\u043f\u043e\u0440\u0430<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u041f\u0440\u0430\u0432\u0438\u043b\u043e \u0448\u0442\u043e\u043f\u043e\u0440\u0430 \u0438\u043b\u0438 \u0432\u0438\u043d\u0442\u0430<\/strong> \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043f\u0440\u0430\u0432\u0438\u043b\u0443 \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0432\u0441\u044f \u043b\u0430\u0434\u043e\u043d\u044c. \u041f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f:<\/p>\n<ol style=\"color:#ff6f00; font-weight: bold;>\n<li><span style=\" color:#262626;font-weight:=\"\" normal;\"=\"\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#000000;font-weight: normal;\">\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0441\u0432\u043e\u0435 \u0432\u043e\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u0438\u0435, \u043f\u043e\u043c\u0435\u0441\u0442\u0438\u0442\u0435 \u0448\u0442\u043e\u043f\u043e\u0440 (\u0438\u043b\u0438 \u0432\u0438\u043d\u0442) \u0442\u0430\u043a, \u0447\u0442\u043e\u0431\u044b \u0435\u0433\u043e \u0440\u0443\u0447\u043a\u0430 \u0431\u044b\u043b\u0430 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0430 \u0432 \u0442\u043e\u043c \u0436\u0435 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0438, \u0447\u0442\u043e \u0438 \u043f\u0435\u0440\u0432\u044b\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a13b5c3a9f833efc0ddf4caf790f0483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#000000;font-weight: normal;\">\u0417\u0430\u0442\u0435\u043c \u043f\u043e\u0432\u0435\u0440\u043d\u0438\u0442\u0435 \u0448\u0442\u043e\u043f\u043e\u0440 \u043a\u043e \u0432\u0442\u043e\u0440\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c87e248254db96e4d2c996a62911e87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{v}})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> \u043a\u0430\u043a \u0431\u0443\u0434\u0442\u043e \u0441\u043e\u0431\u0438\u0440\u0430\u0435\u0448\u044c\u0441\u044f \u0437\u0430\u0442\u043a\u043d\u0443\u0442\u044c \u0435\u0433\u043e \u043f\u0440\u043e\u0431\u043a\u043e\u0439. \u0412\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043f\u043e\u0432\u0435\u0440\u043d\u0443\u0442\u044c \u0448\u0442\u043e\u043f\u043e\u0440 \u0432 \u0442\u0443 \u0441\u0442\u043e\u0440\u043e\u043d\u0443, \u0433\u0434\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438 \u043d\u0430\u0438\u043c\u0435\u043d\u044c\u0448\u0435\u0435.<\/li>\n<li> <span style=\"color:#000000;font-weight: normal;\">\u041d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u0441\u043f\u0438\u0440\u0430\u043b\u044c \u0448\u0442\u043e\u043f\u043e\u0440\u0430, \u0431\u0443\u0434\u0435\u0442 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f.\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2fce88450a631ec24e37f45befae0675_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\vv{\\text{u}}\\times\\vv{\\text{v}}).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"58\" style=\"vertical-align: -5px;\"><\/p>\n<p><\/span> <\/li>\n<\/ol>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/regle-du-tire-bouchon-ou-de-la-vis.webp\" alt=\"\u0448\u0442\u043e\u043f\u043e\u0440 \u0438\u043b\u0438 \u0432\u0438\u043d\u0442\u043e\u0432\u0430\u044f \u043b\u0438\u043d\u0435\u0439\u043a\u0430\" class=\"wp-image-902\" width=\"327\" height=\"500\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-producto-vectorial-de-dos-vectores\"><\/span> \u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0438\u043c\u0435\u0435\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0445\u0430\u0440\u0430\u043a\u0442\u0435\u0440\u0438\u0441\u0442\u0438\u043a\u0438:<\/p>\n<ul>\n<li> <strong>\u0410\u043d\u0442\u0438\u043a\u043e\u043c\u043c\u0443\u0442\u0430\u0442\u0438\u0432\u043d\u043e\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e:<\/strong> \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0432\u0445\u043e\u0434\u044f\u0449\u0438\u0445 \u0432 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435, \u043d\u0435 \u0431\u0435\u0437\u0440\u0430\u0437\u043b\u0438\u0447\u0435\u043d, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0432 \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e\u0441\u0442\u0438 \u043e\u0442 \u043d\u0435\u0433\u043e \u043c\u0435\u043d\u044f\u0435\u0442\u0441\u044f \u0437\u043d\u0430\u043a.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da6aeea2768e41a7e3630dc83ff1e31b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\times\\vv{\\text{v}} = - \\vv{\\text{v}}\\times\\vv{\\text{u}}\" title=\"Rendered by QuickLaTeX.com\" height=\"9\" width=\"119\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>\u0420\u0430\u0441\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e<\/strong> \u0441\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u0438 \u0432\u044b\u0447\u0438\u0442\u0430\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bfddca49d7ded207f392f54341fff56d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\times(\\vv{\\text{v}}+\\vv{\\text{w}}) = \\vv{\\text{u}}\\times\\text{v}}+\\vv{\\text{u}}\\times \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"220\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-68e08abafcbf4b05614819ca1a364a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}\\times(\\vv{\\text{v}}-\\vv{\\text{w}}) = \\vv{\\text{u}}\\times\\text{v}}-\\vv{\\text{u}}\\times \\vv{\\text{w}}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"220\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>\u0421\u0432\u043e\u0439\u0441\u0442\u0432\u043e \u043e\u0434\u043d\u043e\u0440\u043e\u0434\u043d\u043e\u0441\u0442\u0438<\/strong> : \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043d\u0430 \u0441\u043a\u0430\u043b\u044f\u0440 (\u0434\u0435\u0439\u0441\u0442\u0432\u0438\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0447\u0438\u0441\u043b\u043e) \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044e \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043d\u0430 \u0443\u043a\u0430\u0437\u0430\u043d\u043d\u044b\u0439 \u0441\u043a\u0430\u043b\u044f\u0440.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ee3552bb6b72db4d30b4aa9f73e99a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k \\cdot (\\vv{\\text{u}}\\times\\vv{\\text{v}}) =  (k\\cdot \\vv{\\text{u}})\\times\\vv{\\text{v}}=\\vv{\\text{u}}\\times(k\\cdot\\vv{\\text{v}})\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"278\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0412\u0435\u043a\u0442\u043e\u0440, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0439 \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, <strong>\u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d<\/strong> \u0434\u0432\u0443\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c, \u0443\u0447\u0430\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u043c \u0432 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a96345e09a0fdb952557c9138c72ac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} \\vv{\\text{u}} \\perp (\\vv{\\text{u}}\\times\\vv{\\text{v}}) \\\\[2ex] \\vv{\\text{v}} \\perp (\\vv{\\text{u}}\\times\\vv{\\text{v}}) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"87\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0435\u0441\u043b\u0438 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043e\u0440\u0442\u043e\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u044b, \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u044e\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d49d463798c6381c9a8c065417ee3dbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\perp \\vv{\\text{v}} \\ \\longrightarrow \\ \\begin{cases} \\vv{\\text{u}} \\cdot (\\vv{\\text{u}}\\times\\vv{\\text{v}})=0 \\\\[2ex] \\vv{\\text{v}} \\cdot (\\vv{\\text{u}}\\times\\vv{\\text{v}})=0 \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"220\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 <strong>\u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<\/strong> \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u0435\u0432\u043e\u043c\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 (\u0438\u043b\u0438 \u043d\u0443\u043b\u044e).<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5a2e4e335c132d024b2932139a51f101_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\ || \\ \\vv{\\text{v}} \\ \\longrightarrow \\ \\vv{\\text{u}}\\times\\vv{\\text{v}}=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0415\u0441\u043b\u0438 \u043c\u044b \u043d\u0435 \u0437\u043d\u0430\u0435\u043c \u0443\u0433\u043e\u043b, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438, \u043c\u043e\u0434\u0443\u043b\u044c \u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u0436\u0435 \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u043c\u0443 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044e: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f27e24e2a7310fb1e727891c17de911a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}}\\times\\vv{\\text{v}} \\rvert = \\sqrt{ \\lvert \\vv{\\text{u}}\\rvert ^2 \\cdot \\lvert \\vv{\\text{v}} \\rvert ^2 - (\\vv{\\text{u}}\\cdot \\vv{\\text{v}})^2 \\vphantom{\\frac{1}{2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"233\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calcular-el-area-de-un-paralelogramo-o-un-triangulo-mediante-el-producto-vectorial\"><\/span> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430 \u0438\u043b\u0438 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0435\u0442 \u0441 \u043f\u043b\u043e\u0449\u0430\u0434\u044c\u044e \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430, \u0443 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044d\u0442\u0438 \u0434\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u0442\u043e\u0440\u043e\u043d\u0430\u043c\u0438. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, <strong>\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0449\u0430\u0434\u0438 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430.<\/strong> <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-vectoriel-de-deux-vecteurs-dans-lespace.webp\" alt=\"\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0432 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435\" class=\"wp-image-929\" width=\"300\" height=\"173\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430 \u0434\u0435\u043b\u0438\u0442 \u0435\u0433\u043e \u043d\u0430 \u0434\u0432\u0430 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u0438\u043b\u0438, \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u0441\u043b\u043e\u0432\u0430\u043c\u0438, \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \u2014 \u044d\u0442\u043e \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0430 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430. \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, <strong>\u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430<\/strong> \u0440\u0430\u0432\u043d\u0430 \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0435 \u043c\u043e\u0434\u0443\u043b\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u043f\u0440\u0438\u043d\u044f\u0432\u0448\u0435\u0433\u043e \u0434\u0432\u0435 \u0435\u0433\u043e \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u043a\u0430\u043a \u0432\u0435\u043a\u0442\u043e\u0440\u044b. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-vectoriel-de-deux-vecteurs-dans-r2.webp\" alt=\"\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0432 r2\" class=\"wp-image-927\" width=\"300\" height=\"173\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> \u041d\u0430\u043f\u043e\u043c\u043d\u0438\u043c, \u0447\u0442\u043e \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0432 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043a\u043e\u0440\u043d\u0435\u043c \u0441\u0443\u043c\u043c\u044b \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u0432 \u0435\u0433\u043e \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8cf7995798482007ea32b809e80a4062_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}} \\rvert =  \\sqrt{\\vphantom{\\frac{1}{2}} \\text{v}_x^2+\\text{v}_y^2+\\text{v}_z^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"155\" style=\"vertical-align: -11px;\"><\/p>\n<\/p>\n<p> \u042d\u0442\u043e \u0434\u0432\u0430 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438. \u041e\u0434\u043d\u0430\u043a\u043e \u0443 \u043d\u0435\u0433\u043e \u0435\u0441\u0442\u044c \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f, \u043d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0432 \u0444\u0438\u0437\u0438\u043a\u0435 \u043e\u043d \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043c\u0430\u0433\u043d\u0438\u0442\u043d\u043e\u0433\u043e \u043f\u043e\u043b\u044f. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-productos-vectoriales-de-vectores\"><\/span> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0438 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1c06e6d75f54661416056d31d409d8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (-1,4,2) \\qquad \\vv{\\text{v}}= (0,-2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0440\u0435\u0448\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 3\u00d73:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-44db63ee02936f6e5f21891c3e412fb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] -1&amp; 4 &amp; 2 \\\\[1.1ex] 0 &amp;-2&amp;1  \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"160\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0431\u0443\u0434\u0435\u043c \u0440\u0435\u0448\u0430\u0442\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0430\u0434\u044a\u044e\u0432\u0430\u043d\u0442\u043e\u0432 \u0438\u043b\u0438 \u043a\u043e\u0444\u0430\u043a\u0442\u043e\u0440\u043e\u0432 (\u043d\u043e \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0438 \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0421\u0430\u0440\u0440\u0443\u0441\u0430):<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fe298c37814c92498e4fd8ade0620951_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] -1&amp; 4 &amp; 2 \\\\[1.1ex] 0 &amp;-2&amp;1\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} 4 &amp; 2 \\\\[1.1ex]-2&amp;1\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  -1&amp; 2 \\\\[1.1ex] 0 &amp;1\\end{vmatrix}+\\vv{z}\\begin{vmatrix}-1&amp; 4 \\\\[1.1ex] 0 &amp;-2\\end{vmatrix}  \\\\[2ex] &amp; = 8\\vv{i}+\\vv{j}+2\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"387\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0431\u0443\u0434\u0435\u0442: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1efe3e9fce5a83e193da24a5ff60835_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\bm{(8,1,2)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-210c7ec7b29e06198c491e83e7825a42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (3,-2,4) \\qquad \\vv{\\text{v}}= (1,5,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0440\u0435\u0448\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c 3 \u00d7 3:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6a23d8e45f9065f70c576e6b8db02465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; -2 &amp; 4 \\\\[1.1ex] 1 &amp;5&amp;-3  \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u0431\u0443\u0434\u0435\u043c \u0438\u0441\u043a\u0430\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0441\u043e\u043f\u0440\u044f\u0436\u0435\u043d\u043d\u044b\u0445 \u0438\u043b\u0438 \u043a\u043e\u0444\u0430\u043a\u0442\u043e\u0440\u043e\u0432 (\u0445\u043e\u0442\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0421\u0430\u0440\u0440\u0443\u0441\u0430 \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u0432\u0437\u0430\u0438\u043c\u043e\u0437\u0430\u043c\u0435\u043d\u044f\u0435\u043c\u043e):<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-02ffb40666893faa7677234065f3f85f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 3&amp; -2 &amp; 4 \\\\[1.1ex] 1 &amp;5&amp;-3\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} -2 &amp; 4 \\\\[1.1ex] 5&amp;-3\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  3&amp; 4 \\\\[1.1ex]  1&amp;-3\\end{vmatrix}+\\vv{z}\\begin{vmatrix}3&amp; -2  \\\\[1.1ex] 1 &amp;5\\end{vmatrix}  \\\\[2ex] &amp; = -14\\vv{i}+13\\vv{j}+17\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"386\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0431\u0443\u0434\u0435\u0442: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8f7c253fdd7c5be3635a42a3826acfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}}=\\bm{(-14,13,17)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u0417\u043d\u0430\u044f \u043c\u043e\u0434\u0443\u043b\u0438 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0438 \u0443\u0433\u043e\u043b, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u043d\u0438 \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b632ab1324e7ece2d4c1f5c54249b425_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|\\vv{\\text{u}}|= 5 \\qquad |\\vv{\\text{v}}|= 6 \\qquad \\alpha = 30\u00ba\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"226\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. <\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041c\u044b \u043c\u043e\u0436\u0435\u043c \u043b\u0435\u0433\u043a\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u043e\u0434\u0443\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438, \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u0432 \u0444\u043e\u0440\u043c\u0443\u043b\u0443: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-06dcff41e0dcf31152f0047507056f24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert &amp; = \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}}\\rvert \\cdot \\text{sen}(\\alpha) \\\\[2ex] &amp; = 5 \\cdot 6 \\cdot \\text{sen}(30\u00ba) \\\\[2ex] &amp;= 30 \\cdot 0,5 \\\\[2ex] &amp;= \\bm{15} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"140\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<p> \u0418\u0437 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0438\u0445\u0441\u044f \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u044d\u043a\u0440\u0430\u043d\u0430: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-vectoriel-en-ligne-de-deux-vecteurs.webp\" alt=\"\u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0432 \u0441\u0442\u0440\u043e\u043a\u0435\" class=\"wp-image-938\" width=\"151\" height=\"231\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0443, \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u0441\u043c\u044b\u0441\u043b \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0439 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-facaf3cf3a645b725e61c9fcb195e53c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0414\u0432\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043d\u043e\u0440\u043c\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0431\u0443\u0434\u0435\u0442:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8f675fe7eb44c050c508c4771c0a439_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}}\\rvert &amp; = \\lvert \\vv{\\text{u}} \\rvert \\cdot \\lvert \\vv{\\text{v}}\\rvert \\cdot \\text{sen}(\\alpha) \\\\[2ex] &amp; = 3 \\cdot 4 \\cdot \\text{sen}(90\u00ba) \\\\[2ex] &amp;= 12 \\cdot 1 \\\\[2ex] &amp;= \\bm{12} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"140\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u0432\u0435\u043a\u0442\u043e\u0440, \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0439 \u0432 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u0434\u0432\u0443\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c, \u0443\u0447\u0430\u0441\u0442\u0432\u0443\u044e\u0449\u0438\u043c \u0432 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438, <strong>\u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0435\u0433\u043e \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0431\u0443\u0434\u0435\u0442 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e \u044d\u043a\u0440\u0430\u043d\u0443.<\/strong><\/p>\n<p class=\"has-text-align-left\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \u043b\u0438\u043d\u0438\u0438 (\u0438\u043b\u0438 \u0448\u0442\u043e\u043f\u043e\u0440\u0430), \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0432\u044b\u0432\u043e\u0434, \u0447\u0442\u043e <strong>\u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0438\u0440\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0431\u0443\u0434\u0435\u0442 \u0432\u043d\u0443\u0442\u0440\u044c \u044d\u043a\u0440\u0430\u043d\u0430.<\/strong><\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 5<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430, \u0434\u0432\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u0438\u043c\u0435\u044e\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u044b: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43326a03cb829fb91d8c265bddf92b8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (2,3,-2) \\qquad \\vv{\\text{v}}= (5,0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041f\u043b\u043e\u0449\u0430\u0434\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u043e\u0433\u0440\u0430\u043c\u043c\u0430 \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u0435\u0442 \u0441 \u043c\u043e\u0434\u0443\u043b\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0435\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0449\u0438\u0445. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e7c1825be82d94c4eae49c73f509858_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}}\\times \\vv{\\text{v}} = \\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex]2&amp; 3 &amp; -2 \\\\[1.1ex] 5 &amp;0&amp;-1\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} 3 &amp; -2 \\\\[1.1ex] 0&amp;-1\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  2&amp; -2 \\\\[1.1ex] 5 &amp;-1\\end{vmatrix}+\\vv{z}\\begin{vmatrix}2&amp; 3  \\\\[1.1ex] 5 &amp;0\\end{vmatrix}  \\\\[2ex] &amp; = -3\\vv{i}-8\\vv{j}-15\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"411\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u0437\u0430\u0442\u0435\u043c \u0432\u0430\u0448 \u043c\u043e\u0434\u0443\u043b\u044c: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-164e46102f5d27babfec98f25d479fab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\lvert\\vv{\\text{u}}\\times \\vv{\\text{v}} \\rvert = \\sqrt{\\vphantom{\\frac{1}{2}} (-3)^2+(-8)^2+(-15)^2}=\\bm{17,26} \\ \\mathbf{u}\\bm{^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"404\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 6<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430, \u0432\u0435\u0440\u0448\u0438\u043d\u0430\u043c\u0438 \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u0442\u043e\u0447\u043a\u0438: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc08f9ac339b7ac3787a449cf5558c68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,1,0) \\qquad B(4,0,3)\\qquad C(-1,2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"294\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>\u041f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u041f\u0440\u0435\u0436\u0434\u0435 \u0432\u0441\u0435\u0433\u043e, \u043c\u044b \u0434\u043e\u043b\u0436\u043d\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u044b, \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0449\u0438\u0435 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f7661fc5ae3b35c76e0fe98203258962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B- A = (4,0,3)-(2,1,0) = (2,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"351\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5d3f55a240188777fdbb3d74cbf4f61f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{BC} =C- B =(-1,2,3)- (4,0,3) = (-5,2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"366\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0440\u0430\u0432\u043d\u0430 \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0435 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0435\u0433\u043e \u043e\u0431\u0440\u0430\u0437\u0443\u044e\u0449\u0438\u0445. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42a0ae5858bcb681ee92ec1ed67424c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\vv{\\text{u}}\\times \\vv{\\text{v}} = \\begin{vmatrix}\\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex]2&amp; -1 &amp; 3 \\\\[1.1ex] -5 &amp;2&amp;0\\end{vmatrix} &amp; = \\vv{i}\\begin{vmatrix} -1 &amp; 3 \\\\[1.1ex] 2&amp;0\\end{vmatrix} -\\vv{j}\\begin{vmatrix}  2&amp;  3 \\\\[1.1ex] -5 &amp;0\\end{vmatrix}+\\vv{z}\\begin{vmatrix}2&amp; -1  \\\\[1.1ex] -5 &amp;2\\end{vmatrix}  \\\\[2ex] &amp; = -6\\vv{i}-15\\vv{j}-\\vv{z}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"453\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u043b\u0435 \u0432\u0430\u0448\u0435\u0433\u043e \u043c\u043e\u0434\u0443\u043b\u044f:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a52c4a997a5b68d67b9ae52ca599661_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert\\vv{\\text{u}}\\times \\vv{\\text{v}} \\rvert = \\sqrt{\\vphantom{\\frac{1}{2}} (-6)^2+(-15)^2+(-1)^2}=16,19\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"342\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0418 \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0431\u0443\u0434\u0435\u0442 \u0440\u0430\u0432\u043d\u0430 \u043f\u043e\u043b\u043e\u0432\u0438\u043d\u0435 \u043c\u043e\u0434\u0443\u043b\u044f: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b56f201265ba609f4b7c75f486120fc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A=\\cfrac{1}{2}\\cdot  \\lvert\\vv{\\text{u}}\\times \\vv{\\text{v}} \\rvert = \\cfrac{1}{2}\\cdot 16,19=\\bm{8,09} \\ \\mathbf{u}\\bm{^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"284\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442\u0441\u044f, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0438 \u043a\u0430\u043a \u043e\u043d\u043e \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u0443\u0432\u0438\u0434\u0438\u0442\u0435, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0438 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u043f\u0440\u0430\u0432\u043e\u0439 \u0440\u0443\u043a\u0438 (\u0438\u043b\u0438 \u0448\u0442\u043e\u043f\u043e\u0440). \u0411\u043e\u043b\u0435\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u043d\u0430\u0439\u0434\u0435\u0442\u0435 \u0441\u043f\u043e\u0441\u043e\u0431\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u044d\u0442\u043e\u0433\u043e \u0442\u0438\u043f\u0430 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439, \u0430 \u0442\u0430\u043a\u0436\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0438 \u0437\u0430\u0434\u0430\u0447\u0438, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0435 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c. \u0427\u0435\u043c\u0443 \u0440\u0430\u0432\u043d\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432? &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%bd%d0%be%d0%b5-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b5-%d0%b4%d0%b2%d1%83%d1%85-%d0%b2%d0%b5%d0%ba%d1%82%d0%be%d1%80%d0%be\/\"> <span class=\"screen-reader-text\">\u041f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u043f\u0435\u0440\u0435\u043a\u0440\u0435\u0441\u0442\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435)<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[22],"tags":[],"class_list":["post-74","post","type-post","status-publish","format-standard","hentry","category-22"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u043f\u0440\u0438\u043c\u0435\u0440\u044b)<\/title>\n<meta name=\"description\" content=\"\u041e\u0431\u044a\u044f\u0441\u043d\u0435\u043d\u0438\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432. \u0421 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u043c\u0438 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f\u043c\u0438 \u043d\u0430 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