{"id":716,"date":"2023-07-07T19:40:14","date_gmt":"2023-07-07T16:40:14","guid":{"rendered":"https:\/\/bagrut-ru.com\/?p=716"},"modified":"2025-09-04T17:43:41","modified_gmt":"2025-09-04T14:43:41","slug":"%d0%b1%d0%b0%d0%b3%d1%80%d1%83%d1%82-5-%d0%bb%d0%b5%d1%82%d0%be-2023-%d0%b2%d0%b0%d1%80%d0%b8%d0%b0%d0%bd%d1%82-35582-%d0%b7%d0%b0%d0%b4%d0%b0%d0%bd%d0%b8%d0%b5-2","status":"publish","type":"post","link":"https:\/\/bagrut-ru.com\/?p=716","title":{"rendered":"\u0411\u0410\u0413\u0420\u0423\u0422 (5). \u041b\u0415\u0422\u041e 2023, \u0412\u0410\u0420\u0418\u0410\u041d\u0422 35582, \u0417\u0410\u0414\u0410\u041d\u0418\u0415 2"},"content":{"rendered":"\n
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\"\"<\/figure>\n<\/figure>\n\n\n\n
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\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/a><\/p>\n\n\n\n

\n\t\t\t\t
\u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/div>\n\t\t\t\t
<\/p>\n\n\n\n
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(\u05d0)<\/mark><\/strong> \u0414\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u044c \\(CA’\\) \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(BC’D\\).<\/p>\n\n\n\n

\u041f\u0440\u044f\u043c\u0430\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u0435\u0441\u043b\u0438 \u043e\u043d\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0430 \u0434\u0432\u0443\u043c \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u043c\u0441\u044f \u043f\u0440\u044f\u043c\u044b\u043c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438. <\/em><\/p>\n\n\n\n

\u0420\u0435\u0431\u0440\u0430 \u043a\u0443\u0431\u0430, \u0432\u044b\u0445\u043e\u0434\u044f\u0449\u0438\u0435 \u0438\u0437 \u043e\u0434\u043d\u043e\u0439 \u0432\u0435\u0440\u0448\u0438\u043d\u044b \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{ AB}\\), \\(\\overrightarrow{ AD}\\), \\(\\overrightarrow{ AA’}\\) \u043f\u043e\u043f\u0430\u0440\u043d\u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b. \u0441\u043c. \u0440\u0438\u0441. 1<\/p>\n\n\n\n

\u0421\u043a\u0430\u043b\u044f\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\u044b\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e.<\/em> \u0417\u043d\u0430\u0447\u0438\u0442, \\(\\underline{u} \\cdot \\underline{v}=\\underline{u} \\cdot \\underline{w}=\\underline{v} \\cdot \\underline{w}=0\\)<\/p>\n\n\n\n

\u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0434\u043b\u0438\u043d\u044b \u044d\u0442\u0438\u0445 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432 \u0440\u0430\u0432\u043d\u044b, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \\( \\underline{u}^2=\\underline{v}^2=\\underline{w}^2\\)<\/p>\n\n\n\n

\u0427\u0442\u043e\u0431\u044b \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u044c \\(CA’\\) \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(BC’D\\), \u0434\u043e\u043a\u0430\u0436\u0435\u043c, \u0447\u0442\u043e \u0432\u0435\u043a\u0442\u043e\u0440 \\(\\overrightarrow{ CA’ }\\) \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u0435\u043d \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c \\(\\overrightarrow{ C’D }\\) \u0438 \\(\\overrightarrow{ C’B }\\). \u0412\u044b\u0440\u0430\u0437\u0438\u043c \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{ CA’ }\\) ,\\(\\overrightarrow{ C’D }\\) \u0438 \\(\\overrightarrow{ C’B }\\) \u0447\u0435\u0440\u0435\u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\underline{u},\\ \\underline{v},\\ \\underline{w}\\).<\/p>\n\n\n\n

\\(\\overrightarrow{ CA’ }=\\overrightarrow{ AA’ }-\\overrightarrow{ AC}=\\underline{w}-(\\underline{v}+\\underline{u})=\\underline{w}-\\underline{v}-\\underline{u}\\)<\/p>\n\n\n\n

\\(\\overrightarrow{ DC }=\\overrightarrow{ AB}=\\underline{u}\\). \\(\\overrightarrow{ BC }=\\overrightarrow{ AD}=\\underline{v}\\)<\/p>\n\n\n\n

\u0422\u043e\u0433\u0434\u0430 \\(\\overrightarrow{ C’D } =-\\overrightarrow{ DC’ }=-(\\underline{u}+\\underline{w})\\). \\(\\overrightarrow{ C’B } =-\\overrightarrow{ BC’ }=-(\\underline{v}+\\underline{w})\\)<\/p>\n\n\n\n

\\(\\overrightarrow{ CA’ }\\cdot \\overrightarrow{ C’D }=\\)<\/p>\n\n\n\n

\\(=(\\underline{w}-\\underline{v}-\\underline{u})\\cdot (-\\underline{u}-\\underline{w})=\\)<\/p>\n\n\n\n

\\(=-\\underline{u}\\cdot \\underline{w}+\\underline{v}\\cdot \\underline{u}+(\\underline{u})^2-(\\underline{w})^2+\\underline{v} \\cdot \\underline{w}+\\underline{u}\\cdot \\underline{w}=\\)<\/p>\n\n\n\n

\\(=0\\), \u0442\u0430\u043a \u043a\u0430\u043a \\(\\underline{u}^2=\\underline{w}^2\\). <\/p>\n\n\n\n

\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{ CA’ }\\) \u0438 \\( \\overrightarrow{ C’D }\\) \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0438 \u043e\u0442\u0441\u044e\u0434\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b \u043f\u0440\u044f\u043c\u044b\u0435 \\(CA’ \\) \u0438 \\(C’D \\). <\/p>\n\n\n\n

\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u0434\u043e\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e\u0441\u0442\u044c \u043f\u0440\u044f\u043c\u044b\u0445 \\(CA’ \\) \u0438 \\(C’B \\). <\/p>\n\n\n\n

\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0434\u0438\u0430\u0433\u043e\u043d\u0430\u043b\u044c \\(CA’\\) \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0430 \u0434\u0432\u0443\u043c \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u044e\u0449\u0438\u043c\u0441\u044f \u043f\u0440\u044f\u043c\u044b\u043c \\(CA’ \\) \u0438 \\(C’D \\), \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u043d\u0430 \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(BC’D\\). <\/p>\n<\/div>\n\n\n\n

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\u0440\u0438\u0441. 1<\/figcaption><\/figure>\n<\/figure>\n\n\n\n
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\u0440\u0438\u0441. 2<\/figcaption><\/figure>\n<\/figure>\n\n\n\n
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\u0440\u0438\u0441. 3<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n
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(\u05d1)<\/mark><\/strong> (1) \u0422\u043e\u0447\u043a\u0430 \\(E\\) — \u0442\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043c\u0435\u0434\u0438\u0430\u043d \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \\(BC’D\\). \u0422\u043e\u0447\u043a\u0430 \u043f\u0435\u0440\u0435\u0441\u0435\u0447\u0435\u043d\u0438\u044f \u043c\u0435\u0434\u0438\u0430\u043d \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \u0434\u0435\u043b\u0438\u0442 \u043c\u0435\u0434\u0438\u0430\u043d\u0443 \u0432 \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u0438 2:1, \u0441\u0447\u0438\u0442\u0430\u044f \u043e\u0442 \u0432\u0435\u0440\u0448\u0438\u043d\u044b. \u041f\u0443\u0441\u0442\u044c \u0442\u043e\u0447\u043a\u0430 \\(O \\) — \u0441\u0435\u0440\u0435\u0434\u0438\u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0430 \\(BD\\), \u0442\u043e\u0433\u0434\u0430 \\(C’O\\) — \u043c\u0435\u0434\u0438\u0430\u043d\u0430 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a\u0430 \\(BC’D\\), \u0438 \\(C’E=\\frac{2}{3}C’O\\). \u041e\u0442\u0441\u044e\u0434\u0430:<\/p>\n\n\n\n

\\(\\overrightarrow{C’E}=\\frac{2}{3}\\overrightarrow{C’O}\\)<\/p>\n\n\n\n

\u0412\u044b\u0440\u0430\u0437\u0438\u043c \u0432\u0435\u043a\u0442\u043e\u0440 \\(\\overrightarrow{C’E}\\) \u0447\u0435\u0440\u0435\u0437 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\underline{u},\\ \\underline{v},\\ \\underline{w}\\).<\/p>\n\n\n\n

\\(\\overrightarrow{C’O}=\\frac{1}{2}(\\overrightarrow{C’D}+\\overrightarrow{C’B})=\\frac{1}{2}(-\\underline{u}-\\underline{w}-\\underline{v}-\\underline{w})=\\frac{1}{2}(-\\underline{u}-\\underline{v}-2\\underline{w})\\)<\/p>\n\n\n\n

\\(\\overrightarrow{C’E}=\\frac{2}{3}\\overrightarrow{C’O}=\\frac{2}{3}\\cdot \\frac{1}{2}(-\\underline{u}-\\underline{v}-2\\underline{w})= \\frac{1}{3}(-\\underline{u}-\\underline{v}-2\\underline{w})\\)<\/p>\n\n\n\n

\\(\\overrightarrow{CE}=\\overrightarrow{CC’}+\\overrightarrow{C’E}=\\underline{w}+\\frac{1}{3}(-\\underline{u}-\\underline{v}-2\\underline{w})=\\frac{-\\underline{u}-\\underline{v}+\\underline{w}}{3}\\)<\/p>\n\n\n\n

\u041e\u0442\u0432\u0435\u0442: \\(-\\frac{-\\underline{u}-\\underline{v}+\\underline{w}}{3}\\)<\/p>\n<\/div>\n\n\n\n

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\u0440\u0438\u0441. 4<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<\/div>\n\n\n\n

(\u05d1)<\/mark><\/strong> (2) \u0422\u043e\u0447\u043a\u0438 \\(C, \\ E,\\ A’\\) \u043b\u0435\u0436\u0430\u0442 \u043d\u0430 \u043e\u0434\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439, \u0435\u0441\u043b\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{CE}\\) \u0438 \\(\\overrightarrow{CA’}\\) \u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u044b. <\/p>\n\n\n\n

\u0412\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{a}\\) \u0438 \\(\\overrightarrow{b}\\) \u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u044b, \u0435\u0441\u043b\u0438 \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0442\u0430\u043a\u043e\u0435 \u0447\u0438\u0441\u043b\u043e \\(k\\), \u0447\u0442\u043e \\(\\overrightarrow{a}=k\\cdot \\overrightarrow{b}\\)<\/em><\/p>\n\n\n\n

\\(\\overrightarrow{CE}=\\frac{-\\underline{u}-\\underline{v}+\\underline{w}}{3}\\), \\(\\overrightarrow{ CA’ }=\\underline{w}-\\underline{v}-\\underline{u}\\). \u041e\u0442\u0441\u044e\u0434\u0430 \\(\\overrightarrow{CE}=\\frac{1}{3}\\overrightarrow{ CA’ }\\). <\/p>\n\n\n\n

\u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{CE}\\) \u0438 \\(\\overrightarrow{CA’}\\) \u043a\u043e\u043b\u043b\u0438\u043d\u0435\u0430\u0440\u043d\u044b, \u0438, \u0437\u043d\u0430\u0447\u0438\u0442, \u0442\u043e\u0447\u043a\u0438 \\(C, \\ E,\\ A’\\) \u043b\u0435\u0436\u0430\u0442 \u043d\u0430 \u043e\u0434\u043d\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439<\/p>\n\n\n\n

(\u05d2)<\/mark><\/strong> (1) \u041d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(A(4,n,p)\\) \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438, \u0447\u0442\u043e \\(D(0,0,0)\\), \\(C(3,4,0)\\). <\/p>\n\n\n\n

\\(\\overrightarrow{DA}\\perp \\overrightarrow{DC}\\), \\(|\\overrightarrow{DA}|=|\\overrightarrow{DC}|\\)<\/p>\n\n\n\n

\u0412\u0435\u043a\u0442\u043e\u0440\u044b \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0435\u0441\u043b\u0438 \u0438\u0445 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u043d\u0443\u043b\u044e. \u0421\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0435 \u0440\u0430\u0432\u043d\u043e \u0441\u0443\u043c\u043c\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u0435\u0434\u0435\u043d\u0438\u0439 \u043e\u0434\u043d\u043e\u0438\u043c\u0435\u043d\u043d\u044b\u0445 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442. \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430, \u043d\u0443\u0436\u043d\u043e \u0438\u0437 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442 \u043a\u043e\u043d\u0446\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \u0432\u044b\u0447\u0435\u0441\u0442\u044c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0435\u0433\u043e \u043d\u0430\u0447\u0430\u043b\u0430. <\/em><\/p>\n\n\n\n

\\(\\overrightarrow{DA}(4,n,p)\\), \\(\\overrightarrow{DC}(3,4,0)\\)<\/p>\n\n\n\n

\\(\\overrightarrow{DA}\\cdot \\overrightarrow{DC}=4\\cdot 3+n\\cdot 4+p\\cdot 0=0\\)<\/p>\n\n\n\n

\\(12+4n=0,\\ n=-3\\)<\/p>\n\n\n\n

\\(|\\overrightarrow{DA}|=\\sqrt{4^2+n^2+p^2}=\\sqrt{4^2+(-3)^2+p^2}=\\sqrt{25+p^2}\\)<\/p>\n\n\n\n

\\(|\\overrightarrow{DC}|=\\sqrt{3^2+(4)^2+0^2}=\\sqrt{25}=5\\) (***)<\/mark><\/p>\n\n\n\n

\u0422\u0430\u043a \u043a\u0430\u043a \\(|\\overrightarrow{DA}|=|\\overrightarrow{DC}|\\), \\(\\sqrt{25+p^2}=\\sqrt{25}\\). <\/p>\n\n\n\n

\u041e\u0442\u0441\u044e\u0434\u0430 \\(p=0\\). <\/p>\n\n\n\n

\u0422\u043e\u0433\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(A(4,-3,0)\\)<\/p>\n\n\n\n

\u041e\u0442\u0432\u0435\u0442: <\/em> \\(A(4,-3,0)\\)<\/p>\n\n\n\n

\u0422\u043e\u0447\u043a\u0438 \\(A(4,-3,0)\\), \\(D(0,0,0)\\), \\(C(3,4,0)\\) \u043b\u0435\u0436\u0430\u0442 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(z=0\\), \\(AB\\| DC\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0440\u044f\u043c\u0430\u044f \\(AB\\) \u0442\u0430\u043a\u0436\u0435 \u043b\u0435\u0436\u0438\u0442 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(z=0\\). \u041e\u0442\u0441\u044e\u0434\u0430 \u0447\u0435\u0442\u044b\u0440\u0435\u0445\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a \\(ABCD\\) \u043b\u0435\u0436\u0438\u0442 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(z=0\\).<\/p>\n\n\n\n

(\u05d2)<\/mark><\/strong> (2) \u041d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(C’\\) \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438 \u0447\u0442\u043e \\(z>0\\). <\/p>\n\n\n\n

\u0422\u0430\u043a \u043a\u0430\u043a \u0442\u043e\u0447\u043a\u0438 \\(A(4,-3,0)\\), \\(D(0,0,0)\\), \\(C(3,4,0)\\) \u043b\u0435\u0436\u0430\u0442 \u0432 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(z=0\\) (\u0438\u0437 (\u05d2)<\/mark><\/strong> (1)), \u0440\u0435\u0431\u0440\u043e \u043a\u0443\u0431\u0430 \\(\u0421C’\\) \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \\(z=0\\) \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043f\u0435\u0440\u0432\u044b\u0435 \u0434\u0432\u0435 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(C’\\) \u0441\u043e\u0432\u043f\u0430\u0434\u0430\u044e\u0442 \u0441 \u043f\u0435\u0440\u0432\u044b\u043c\u0438 \u0434\u0432\u0443\u043c\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \u0442\u043e\u0447\u043a\u0438 \\(C’\\). \u0422\u043e \u0435\u0441\u0442\u044c \u0442\u043e\u0447\u043a\u0430 \\(C’\\) \u0438\u043c\u0435\u0435\u0442 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \\((3,4,z)\\). <\/p>\n\n\n\n

\u0422\u043e\u0433\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{CC’}(0,0,z)\\).<\/p>\n\n\n\n

\u0414\u043b\u0438\u043d\u0430 \u043e\u0442\u0440\u0435\u0437\u043a\u0430 \\(\u0421C’=5\\) (\u0438\u0437 (***)), \u0442\u0430\u043a \u043a\u0430\u043a \u0432\u0441\u0435 \u0440\u0435\u0431\u0440\u0430 \u043a\u0443\u0431\u0430 \u0438\u043c\u0435\u044e\u0442 \u0440\u0430\u0432\u043d\u044b\u0435 \u0434\u043b\u0438\u043d\u044b. <\/p>\n\n\n\n

\u041e\u0442\u0441\u044e\u0434\u0430 \\(z=5\\).<\/p>\n\n\n\n

\u041e\u0442\u0432\u0435\u0442: \\(C'(3,4,5)\\)<\/p>\n\n\n\n

(\u05d3)<\/mark><\/strong> \u041f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \\(BC’D\\) \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0435\u0442 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \\(BCC’B’\\) \u043f\u043e \u043f\u0440\u044f\u043c\u043e\u0439 \\(l=BC’\\). \u0417\u0430\u043f\u0438\u0448\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u044d\u0442\u043e\u0439 \u043f\u0440\u044f\u043c\u043e\u0439. \u041f\u0440\u044f\u043c\u0430\u044f \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \\(C'(3,4,5)\\), \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u044f\u044e\u0449\u0438\u0439 \u0432\u0435\u043a\u0442\u043e\u0440 \u043f\u0440\u044f\u043c\u043e\u0439 — \u0432\u0435\u043a\u0442\u043e\u0440 \\(\\overrightarrow{C’B}\\)<\/p>\n\n\n\n

\u041d\u0430\u0439\u0434\u0435\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(B(x,y,z)\\)<\/p>\n\n\n\n

\\(\\overrightarrow{AB}=\\overrightarrow{DC}\\), \\(\\overrightarrow{DC}(3,4,0)\\), \\(A(4,-3,0)\\)<\/p>\n\n\n\n

\u0422\u043e\u0433\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{AB}(x-4,y-(-3),0)\\). <\/p>\n\n\n\n

\u0422\u043e\u0433\u0434\u0430: \\(x-4=3, \\ x=7\\), \\(y-(-3)=4,\\ y=1\\). \u041e\u0442\u0441\u044e\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u0430\u043d\u0442\u044b \u0442\u043e\u0447\u043a\u0438 \\(B(7,1,0)\\).
\u041e\u0442\u0441\u044e\u0434\u0430 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0432\u0435\u043a\u0442\u043e\u0440\u0430 \\(\\overrightarrow{C’B}(4, -3, -5)\\). <\/p>\n\n\n\n

\u0422\u043e\u0433\u0434\u0430 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u0440\u044f\u043c\u043e\u0439 \\(l\\) \u043c\u043e\u0436\u043d\u043e \u0437\u0430\u043f\u0438\u0441\u0430\u0442\u044c \u0442\u0430\u043a:<\/p>\n\n\n\n

\u041e\u0442\u0432\u0435\u0442:<\/em> \\((3,4,5)+t(4, -3, -5)\\)<\/p>\n\n\n\n

(\u05d4)<\/mark><\/strong> \u0417\u0430\u043f\u0438\u0448\u0435\u043c \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0441\u043e\u0434\u0435\u0440\u0436\u0438\u0442 \u043f\u0440\u044f\u043c\u0443\u044e \\(l\\) \u0438 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u0435\u043a\u0430\u0435\u0442 \u043e\u0441\u044c \\(X\\) (\u0442\u043e \u0435\u0441\u0442\u044c \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u043e\u0441\u0438 \\(X\\)), \u0430 \u0437\u043d\u0430\u0447\u0438\u0442 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0441 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \\((1,0,0)\\). <\/p>\n\n\n\n

\u041f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u043e\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \\(A(x_0, y_0,z_0)\\) \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u043e \u0432\u0435\u043a\u0442\u043e\u0440\u0430\u043c \\(\\overrightarrow{a}(x_a,y_a,z_a) \\) \u0438 \\(\\overrightarrow{b}(x_b,y_b,z_b) \\) \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434:<\/p>\n\n\n\n

\\((x_0, y_0,z_0)+m(x_a,y_a,z_a)+(x_b,y_b,z_b)\\)<\/mark><\/p>\n\n\n\n

\u041d\u0430\u0448\u0430 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u044c \u043f\u0440\u043e\u0445\u043e\u0434\u0438\u0442 \u0447\u0435\u0440\u0435\u0437 \u0442\u043e\u0447\u043a\u0443 \\(C'(3,4,5)\\), \u043f\u0430\u0440\u0430\u043b\u043b\u0435\u043b\u044c\u043d\u0430 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \\(\\overrightarrow{C’B}(4, -3, -5)\\) \u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u0443 \u0441 \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c\u0438 \\(1,0,0\\), \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u0435\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043c\u043e\u0436\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0432\u0438\u0434:<\/p>\n\n\n\n

\u041e\u0442\u0432\u0435\u0442: <\/em>\\((3,4,5)+m(4, -3, -5)+n(1,0,0)\\)<\/p>\n\n\n\n

<\/div>\n\t\t\t<\/div><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0438\u0441\u0442\u043e\u0447\u043d\u0438\u043a<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-716","post","type-post","status-publish","format-standard","hentry","category-12"],"_links":{"self":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/716","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=716"}],"version-history":[{"count":66,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/716\/revisions"}],"predecessor-version":[{"id":1314,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=\/wp\/v2\/posts\/716\/revisions\/1314"}],"wp:attachment":[{"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=716"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=716"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bagrut-ru.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=716"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}