{"id":217,"date":"2023-07-11T12:27:22","date_gmt":"2023-07-11T12:27:22","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%81%d0%bc%d0%b5%d1%88%d0%b0%d0%bd%d0%bd%d1%8b%d1%85-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b8-%d1%82%d1%80%d0%b5%d1%85\/"},"modified":"2023-07-11T12:27:22","modified_gmt":"2023-07-11T12:27:22","slug":"%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%81%d0%bc%d0%b5%d1%88%d0%b0%d0%bd%d0%bd%d1%8b%d1%85-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b8-%d1%82%d1%80%d0%b5%d1%85","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%81%d0%bc%d0%b5%d1%88%d0%b0%d0%bd%d0%bd%d1%8b%d1%85-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b8-%d1%82%d1%80%d0%b5%d1%85\/","title":{"rendered":"\u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\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 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435) \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 \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u044d\u0442\u043e\u043c\u0443 \u0442\u0438\u043f\u0443 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438. \u0418, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u043e \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u0445 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0438 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-producto-mixto-de-tres-vectores\"><\/span> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/strong> \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0442\u0430\u043a\u0436\u0435 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u043c\u043e\u0435 <strong>\u0442\u0440\u043e\u0439\u043d\u044b\u043c \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u043c \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435\u043c<\/strong> , \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e\u0435 \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0432\u043a\u043b\u044e\u0447\u0430\u044e\u0449\u0435\u0435 \u0434\u0432\u0430 \u0440\u0430\u0437\u043d\u044b\u0445 \u0442\u0438\u043f\u0430 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439:  \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435  \u0438  \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435  . \u0418\u0442\u0430\u043a, \u043a\u043e\u043c\u0431\u0438\u043d\u0430\u0446\u0438\u044f \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u044b\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u0434\u0430\u0435\u0442 \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).<\/p>\n<p> \u041a\u043e\u043d\u043a\u0440\u0435\u0442\u043d\u043e \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0438\u0437 \u0432\u044b\u0447\u0438\u0441\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 \u0434\u0432\u0443\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0438 \u043f\u043e\u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0433\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0433\u043e \u0443\u043c\u043d\u043e\u0436\u0435\u043d\u0438\u044f \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u043e\u0433\u043e \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430 \u043d\u0430 \u0442\u0440\u0435\u0442\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440. \u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043d\u043e\u0435 \u0442\u0430\u043a \u043c\u043e\u0436\u0435\u0442 \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u044c\u0441\u044f \u043e\u0447\u0435\u043d\u044c \u0441\u043b\u043e\u0436\u043d\u044b\u043c, \u043d\u043e \u043d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u044d\u0442\u043e \u043d\u0435 \u0442\u0430\u043a \u0443\u0436 \u0438 \u043c\u043d\u043e\u0433\u043e, \u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0438\u0442\u0435 \u043d\u0430 \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u0442\u0440\u043e\u0439\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\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-7904652c5b12243a6dc713936dba9d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = \\vv{\\text{u}} \\cdot ( \\vv{\\text{v}}\\times \\vv{\\text{w}})\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"163\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> \u041a\u0430\u043a \u0432\u0438\u0434\u043d\u043e \u0432 \u0435\u0433\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435, \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442\u0441\u044f \u0434\u0432\u0443\u043c\u044f \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u044b\u043c\u0438 \u0441\u043a\u043e\u0431\u043a\u0430\u043c\u0438. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-calcular-el-producto-mixto-de-tres-vectores\"><\/span> \u041a\u0430\u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u0442\u0440\u043e\u0439\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u2014 \u044d\u0442\u043e \u0442\u0430, \u043a\u043e\u0442\u043e\u0440\u0443\u044e \u043c\u044b \u0442\u043e\u043b\u044c\u043a\u043e \u0447\u0442\u043e \u0432\u0438\u0434\u0435\u043b\u0438 \u0432 \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c \u0440\u0430\u0437\u0434\u0435\u043b\u0435, \u043e\u0434\u043d\u0430\u043a\u043e \u043e\u043d\u0430 \u043e\u0431\u044b\u0447\u043d\u043e \u043d\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0435\u0441\u0442\u044c \u0434\u0440\u0443\u0433\u043e\u0439, \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u043e\u0439 \u0438 \u0431\u044b\u0441\u0442\u0440\u044b\u0439 \u0441\u043f\u043e\u0441\u043e\u0431: <\/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\"> \u041f\u0443\u0441\u0442\u044c \u043b\u044e\u0431\u044b\u0435 3 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0431\u0443\u0434\u0443\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-3d0daa4c1f9e1aff4f64a39f229bc207_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)\\qquad \\vv{\\text{w}}= (\\text{w}_x,\\text{w}_y,\\text{w}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"431\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> \u0427\u0442\u043e\u0431\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c <strong>\u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432,<\/strong> \u043f\u0440\u043e\u0441\u0442\u043e \u0440\u0435\u0448\u0438\u0442\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c 3\u00d73, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u044b\u0439 \u043a\u043e\u043c\u043f\u043e\u043d\u0435\u043d\u0442\u0430\u043c\u0438 \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-a3fed933d4d02bb5ca6f5bae06ea544d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]=\\begin{vmatrix} \\text{u}_x &amp; \\text{u}_y &amp; \\text{u}_z \\\\[1.1ex] \\text{v}_x &amp;\\text{v}_y&amp;\\text{v}_z \\\\[1.1ex] \\text{w}_x &amp; \\text{w}_y &amp; \\text{w}_z \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"188\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<p> \u0418\u0442\u0430\u043a, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u0443\u0432\u0438\u0434\u0435\u0442\u044c <span style=\"text-decoration: underline;\">\u043f\u0440\u0438\u043c\u0435\u0440 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u044d\u0442\u043e \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f<\/span> , \u043c\u044b \u043d\u0430\u0439\u0434\u0435\u043c \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0442\u0440\u0435\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-d90f4dd611d93b46a9001a7fe26e03f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (1,2,0) \\qquad \\vv{\\text{v}}= (0,-1,3)\\qquad \\vv{\\text{w}}= (-2,4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"369\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0414\u043b\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u044f \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043f\u043e\u0441\u0442\u0440\u043e\u0438\u043c \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, \u0440\u0430\u0441\u043f\u043e\u043b\u043e\u0436\u0438\u0432 \u0432\u0435\u043a\u0442\u043e\u0440\u044b \u0432 \u0441\u0442\u0440\u043e\u043a\u0430\u0445 \u043c\u0430\u0442\u0440\u0438\u0446\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-e5341b4a39b42c1284a4b0129b38b61a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]=\\begin{vmatrix} 1 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; -1 &amp; 3 \\\\[1.1ex] -2 &amp; 4 &amp; 1 \\end{vmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"180\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u043d\u0430\u043c \u043f\u0440\u043e\u0441\u0442\u043e \u043d\u0443\u0436\u043d\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b, \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043c\u043e\u0436\u043d\u043e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c \u043b\u044e\u0431\u043e\u0439 \u043c\u0435\u0442\u043e\u0434. \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u043f\u0440\u0430\u0432\u0438\u043b\u043e \u0421\u0430\u0440\u0440\u0443\u0441\u0430 (\u043d\u043e \u044d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c \u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0434\u043e\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u0439 \u0438\u043b\u0438 \u043a\u043e\u0444\u0430\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-df86565048cf897265878936f2294525_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 1 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; -1 &amp; 3 \\\\[1.1ex] -2 &amp; 4 &amp; 1 \\end{vmatrix} \\\\[2ex] &amp;= -1-12+0-0-12-0 \\\\[2ex] &amp; = \\bm{-25} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"276\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<hr class=\"wp-block-separator has-text-color has-background has-pale-cyan-blue-background-color has-pale-cyan-blue-color is-style-wide\">\n<p> \u0427\u0442\u043e\u0431\u044b \u043f\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u0438 \u0434\u0432\u0435 \u043f\u0440\u043e\u0446\u0435\u0434\u0443\u0440\u044b \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u044b, \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043e\u0434\u043d\u0438\u0445 \u0438 \u0442\u0435\u0445 \u0436\u0435 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u043e\u043c \u0438\u0445 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\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-e4d15d610ca9b4cb39e9f268cfb152ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] &amp; = \\vv{\\text{u}} \\cdot ( \\vv{\\text{v}}\\times \\vv{\\text{w}})\\\\[2ex] &amp;=(1,2,0) \\cdot \\Bigl( (0,-1,3)\\times (-2,4,1)\\Bigr) \\\\[2ex] &amp; = (1,2,0) \\cdot \\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 0&amp; -1 &amp; 3 \\\\[1.1ex] -2 &amp;4&amp;1 \\end{vmatrix} \\\\[2ex] &amp;=  (1,2,0) \\cdot (-13,-6,-2) \\\\[2ex] &amp; = \\bm{-25} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"262\" width=\"332\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u041c\u044b \u0440\u0435\u043a\u043e\u043c\u0435\u043d\u0434\u0443\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0447\u0435\u0440\u0435\u0437 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0442\u0430\u043a \u043a\u0430\u043a \u044d\u0442\u043e \u0431\u044b\u0441\u0442\u0440\u0435\u0435 \u0438 \u043c\u0435\u043d\u044c\u0448\u0435 \u0448\u0430\u043d\u0441\u043e\u0432 \u0434\u043e\u043f\u0443\u0441\u0442\u0438\u0442\u044c \u043e\u0448\u0438\u0431\u043a\u0443. \u041d\u043e, \u043a\u0430\u043a \u0432\u0438\u0434\u0438\u0442\u0435, \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043e\u0434\u0438\u043d \u0438 \u0442\u043e\u0442 \u0436\u0435 \u043d\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043c\u043e \u043e\u0442 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a\u043e\u0439 \u043c\u0435\u0442\u043e\u0434 \u0432\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0435, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0439\u0442\u0435 \u0442\u043e\u0442, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0432\u0430\u043c \u0431\u043e\u043b\u044c\u0448\u0435 \u043d\u0440\u0430\u0432\u0438\u0442\u0441\u044f. \ud83d\udc4d <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"interpretacion-geometrica-del-producto-mixto\"><\/span> \u0413\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0430\u044f \u0438\u043d\u0442\u0435\u0440\u043f\u0440\u0435\u0442\u0430\u0446\u0438\u044f \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u041a\u043e\u0433\u0434\u0430 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0443 \u0432\u0430\u0441 \u043c\u043e\u0436\u0435\u0442 \u0432\u043e\u0437\u043d\u0438\u043a\u043d\u0443\u0442\u044c \u0432\u043e\u043f\u0440\u043e\u0441\u2026 \u0430 \u0434\u043b\u044f \u0447\u0435\u0433\u043e \u043d\u0443\u0436\u043d\u043e \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435? \u0427\u0442\u043e \u0436, \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0435 \u0443 \u043d\u0435\u0433\u043e \u0435\u0441\u0442\u044c \u0434\u0432\u0430 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0445 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f: \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043e\u0431\u044a\u0435\u043c\u0430 \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434\u0430 \u0438 \u043e\u0431\u044a\u0435\u043c\u0430 \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440\u0430.<\/p>\n<p> <strong>\u041e\u0431\u044a\u0435\u043c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434\u0430<\/strong> \u0440\u0430\u0432\u0435\u043d \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043e\u0431\u043e\u0437\u043d\u0430\u0447\u0430\u044e\u0449\u0438\u0445 \u0442\u0440\u0438 \u0438\u0437\u043c\u0435\u0440\u0435\u043d\u0438\u044f \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043f\u043e\u043b\u044f. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-produit-mixte-de-trois-vecteurs.webp\" alt=\"\u043f\u0440\u0438\u043c\u0435\u0440 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f\" class=\"wp-image-999\" width=\"309\" height=\"310\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0414\u0440\u0443\u0433\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u2014 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 <strong>\u043e\u0431\u044a\u0435\u043c\u0430 \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440\u0430<\/strong> . \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0433\u0435\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438 \u0448\u0435\u0441\u0442\u0430\u044f \u0447\u0430\u0441\u0442\u044c \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u0435\u0442 \u0441\u043e\u0431\u043e\u0439 \u043e\u0431\u044a\u0451\u043c \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440\u0430: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/produit-mixte-de-trois-vecteurs-dans-r3.webp\" alt=\"\u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0432 r3\" class=\"wp-image-1002\" width=\"273\" height=\"327\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-del-producto-mixto-o-triple-producto-escalar\"><\/span> \u0421\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0433\u043e \u0441\u043a\u0430\u043b\u044f\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> \u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435, \u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435, \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> \u0412 \u043e\u0431\u0449\u0435\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 <strong>\u043f\u043e\u0440\u044f\u0434\u043a\u0430<\/strong> \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u0436\u0435 \u043f\u043e\u0434\u0440\u0430\u0437\u0443\u043c\u0435\u0432\u0430\u0435\u0442 \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u0437\u043d\u0430\u043a\u0430. \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u043e\u0440\u044f\u0434\u043e\u043a \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0439 \u0432\u0430\u0436\u0435\u043d.<\/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-0ce0eff894cd1fa149c6d8c8ae6f0f03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = -\\bigl[\\vv{\\text{v}},\\vv{\\text{u}},\\vv{\\text{w}}\\bigr] = -\\bigl[\\vv{\\text{u}},\\vv{\\text{w}},\\vv{\\text{v}}\\bigr] = - \\bigl[\\vv{\\text{w}},\\vv{\\text{v}},\\vv{\\text{u}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"356\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li> \u041e\u0434\u043d\u0430\u043a\u043e \u0435\u0441\u043b\u0438 <strong>\u0446\u0438\u043a\u043b\u0438\u0447\u0435\u0441\u043a\u0438<\/strong> \u043c\u0435\u043d\u044f\u0442\u044c \u043f\u043e\u0440\u044f\u0434\u043e\u043a, \u0437\u043d\u0430\u043a \u043d\u0435 \u0438\u0437\u043c\u0435\u043d\u0438\u0442\u0441\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-7e3f514d940b6d366613f59c6cd8bbba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr] = \\bigl[\\vv{\\text{v}},\\vv{\\text{w}},\\vv{\\text{u}}\\bigr] = \\bigl[\\vv{\\text{w}},\\vv{\\text{u}},\\vv{\\text{v}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"229\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<ul>\n<li> \u0412 \u0442\u0440\u0435\u0445\u043c\u0435\u0440\u043d\u043e\u043c \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u0435 (\u0432 R3) \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 <strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e \u0437\u0430\u0432\u0438\u0441\u0438\u043c\u044b\u0445<\/strong> \u0438\u043b\u0438 <strong>\u043a\u043e\u043c\u043f\u043b\u0430\u043d\u0430\u0440\u043d\u044b\u0445<\/strong> \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u043f\u0440\u0438\u043d\u0430\u0434\u043b\u0435\u0436\u0430\u0449\u0438\u0445 \u043e\u0434\u043d\u043e\u0439 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438) \u0440\u0430\u0432\u043d\u043e 0. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-productos-mixtos\"><\/span> \u0418\u0441\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u044b \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u0441\u043e \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u044b\u043c\u0438 \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430\u043c\u0438<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> \u0414\u0430\u043d\u044b 3 \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-e4ea59160804c0287d02cbd1cf01b787_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (3,-1,2) \\qquad \\vv{\\text{v}}= (-2,0,1)\\qquad \\vv{\\text{w}}= (5,1,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"383\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\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-6f6a0d080e09991ca4dc57ff1dd1ab83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -7px;\"><\/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>\u043f\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 \u0435\u0433\u043e \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435, \u043d\u0430\u0434\u043e \u0440\u0435\u0448\u0438\u0442\u044c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c, \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u043d\u044b\u0439 \u0438\u0437 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \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-549ed90889d541ae4a1075449567b062_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 3 &amp; -1 &amp; 2 \\\\[1.1ex] -2 &amp; 0 &amp; 1 \\\\[1.1ex] 5 &amp; 1 &amp; -1 \\end{vmatrix} \\\\[2ex] &amp;= 0-5-4-0-3+2 \\\\[2ex] &amp; = \\bm{-10} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"244\" 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 2<\/h3>\n<p> \u0414\u0430\u043d\u044b 3 \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-269e213cd1d1e52c2189fe0dc420f93b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (7,2,-3) \\qquad \\vv{\\text{v}}= (2,4,9)\\qquad \\vv{\\text{w}}= (4,3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"369\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u044b\u0439 \u043f\u0440\u043e\u0434\u0443\u043a\u0442 \u043c\u0435\u0436\u0434\u0443 \u0442\u0440\u0435\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-6f6a0d080e09991ca4dc57ff1dd1ab83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"56\" style=\"vertical-align: -7px;\"><\/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>\u043f\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 \u0435\u0433\u043e \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435, \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u043d\u0430\u0439\u0442\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u043c\u0435\u0435\u0442 \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 \u0432 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0444\u043e\u0440\u043c\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-29b46155243552a99f6fd75de69f59da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 7 &amp; 2 &amp; -3 \\\\[1.1ex] 2 &amp; 4 &amp; 9 \\\\[1.1ex] 4 &amp; 3 &amp; -1 \\end{vmatrix} \\\\[2ex] &amp;= -28+72-18+48-189+4 \\\\[2ex] &amp; = \\bm{-111} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"312\" 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 3<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043e\u0431\u044a\u0435\u043c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434\u0430, 3 \u0441\u0442\u043e\u0440\u043e\u043d\u044b \u043a\u043e\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0442 \u0441\u043e\u0431\u043e\u0439 \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-897316aad94e2c06a745cc34bdcd2cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}= (0,2,5) \\qquad \\vv{\\text{v}}= (-1,6,2)\\qquad \\vv{\\text{w}}= (3,1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"355\" 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>\u043f\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\"> \u041e\u0431\u044a\u0435\u043c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434\u0430 \u0440\u0430\u0432\u0435\u043d \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0443 \u043d\u0435\u0433\u043e \u0435\u0441\u0442\u044c \u0440\u0435\u0431\u0440\u0430. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \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-9718b369a508216fbb69ab68ac7de381_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 0 &amp; 2 &amp; 5 \\\\[1.1ex] -1 &amp; 6 &amp; 2 \\\\[1.1ex] 3 &amp; 1 &amp; 2 \\end{vmatrix} \\\\[2ex] &amp;= 0+12-5-90-0+4 \\\\[2ex] &amp; = -79 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"263\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u0422\u0430\u043a \u0447\u0442\u043e \u043e\u0431\u044a\u0435\u043c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u0435\u043f\u0438\u043f\u0435\u0434\u0430 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u043e\u0439 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\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-6074917d7c095bd718364a5ed3081c2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= \\lvert -79 \\rvert = \\bm{79}\\ \\mathbf{u}\\bm{^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"145\" 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 4<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043e\u0431\u044a\u0435\u043c \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440\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-4c798eaa40f98c461a076a2bc0aa0910_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,0,2) \\qquad B(3,3,2)\\qquad C(5,-1,4)\\qquad D(4,2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"401\" 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>\u043f\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\"> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u044b, \u043f\u0440\u0435\u0434\u0441\u0442\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0435 \u0440\u0435\u0431\u0440\u0430 \u0442\u0435\u0442\u0440\u0430\u044d\u0434\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-fe16cd346a46022ffcd90ad080b305ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A= (3,3,2)-(1,0,2)=(2,3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"337\" 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-7bb115ce61905a3f3a5c76dfd152b8f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC}=C-A= (5,-1,4)-(1,0,2)=(4,-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"364\" 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-11697d137db244fd5b7a5f6328181183_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AD}=D-A= (4,2,1)-(1,0,2)=(3,2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"353\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> \u041e\u0431\u044a\u0435\u043c \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440\u0430 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u0435\u043d \u043e\u0434\u043d\u043e\u0439 \u0448\u0435\u0441\u0442\u043e\u0439 \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u044f \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043d \u0438\u043c\u0435\u0435\u0442 \u0434\u043b\u044f \u0440\u0435\u0431\u0435\u0440. \u041f\u043e\u044d\u0442\u043e\u043c\u0443 \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0435\u043c \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u043d\u0430\u0439\u0434\u0435\u043d\u043d\u044b\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-d384e76415a756b834e0a8e7c695b1c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\bigl[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{\\text{w}}\\bigr]&amp; =\\begin{vmatrix} 2 &amp; 3 &amp; 0 \\\\[1.1ex] 4 &amp; -1 &amp; 2 \\\\[1.1ex] 3 &amp; 2 &amp; -1 \\end{vmatrix} \\\\[2ex] &amp;= 2+18+0-0-8+12 \\\\[2ex] &amp; = 24 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"262\" 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, \u043e\u0431\u044a\u0435\u043c \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440\u0430 \u0431\u0443\u0434\u0435\u0442 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u044f\u0442\u044c \u043e\u0434\u043d\u0443 \u0448\u0435\u0441\u0442\u0443\u044e \u0430\u0431\u0441\u043e\u043b\u044e\u0442\u043d\u043e\u0439 \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0434\u0443\u043a\u0442\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-0e1aefc732626b5a6d55a904d03452b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"V= \\cfrac{1}{6} \\cdot \\lvert 24 \\rvert = \\cfrac{24}{6} = \\bm{4} \\ \\mathbf{u}\\bm{^3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"189\" 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 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435) \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 \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u044d\u0442\u043e\u043c\u0443 \u0442\u0438\u043f\u0443 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438. \u0418, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u043e \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u0445 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0438 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432? \u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0442\u0430\u043a\u0436\u0435 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d0%bf%d1%80%d0%b8%d0%bc%d0%b5%d1%80%d1%8b-%d1%81%d0%bc%d0%b5%d1%88%d0%b0%d0%bd%d0%bd%d1%8b%d1%85-%d0%bf%d1%80%d0%be%d0%b8%d0%b7%d0%b2%d0%b5%d0%b4%d0%b5%d0%bd%d0%b8%d0%b8-%d1%82%d1%80%d0%b5%d1%85\/\"> <span class=\"screen-reader-text\">\u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\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-217","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>\u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435) \u2014 Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ru\/\u043f\u0440\u0438\u043c\u0435\u0440\u044b-\u0441\u043c\u0435\u0448\u0430\u043d\u043d\u044b\u0445-\u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0438-\u0442\u0440\u0435\u0445\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" 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\u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435) \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 \u043f\u0440\u0438\u043c\u0435\u0440\u044b, \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0438 \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u0437\u0430\u0434\u0430\u0447\u0438 \u043f\u043e \u044d\u0442\u043e\u043c\u0443 \u0442\u0438\u043f\u0443 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439 \u043c\u0435\u0436\u0434\u0443 \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c\u0438. \u0418, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435 \u043e \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u0445 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0438 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0433\u043e \u043f\u0440\u043e\u0434\u0443\u043a\u0442\u0430. \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u0441\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432? \u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0442\u0430\u043a\u0436\u0435 &hellip; \u0421\u043c\u0435\u0448\u0430\u043d\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0442\u0440\u0435\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 (\u0438\u043b\u0438 \u0442\u0440\u043e\u0439\u043d\u043e\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435) \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;","og_url":"https:\/\/mathority.org\/ru\/\u043f\u0440\u0438\u043c\u0435\u0440\u044b-\u0441\u043c\u0435\u0448\u0430\u043d\u043d\u044b\u0445-\u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0438-\u0442\u0440\u0435\u0445\/","article_published_time":"2023-07-11T12:27:22+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7904652c5b12243a6dc713936dba9d6d_l3.png"}],"author":"Mathority \u041a\u043e\u043c\u0430\u043d\u0434\u0430","twitter_card":"summary_large_image","twitter_misc":{"\u041d\u0430\u043f\u0438\u0441\u0430\u043d\u043e \u0430\u0432\u0442\u043e\u0440\u043e\u043c":"Mathority 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