Решите пожалуйста задание!!!. Created by Voproshayka. matematika-ru

Решите пожалуйста задание!!!...

Voproshayka @Voproshayka

July 2022 1 15 Report

Решите пожалуйста задание!!!

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NNNLLL54

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$1a)\; \; M(1,-1,-3)\in l_1\; ,\; \; l_1\parallel\; l_2\\\\l_2:\; \; \frac{x-1}{2}=\frac{y+2}{4}=\frac{z-1}{0} \; \; \to \; \; \; \vec{s}_2=(2,4,0)=\vec{s}_1\\\\l_1:\; \; \frac{x-1}{2}=\frac{x\y+1}{4}=\frac{z+3}{0}\\\\1b)\; \; M(1,-1,-3)\in l_3\; ,\; \; l_3\perp \pi \\\\\pi :\; \; 3x-2y+5z-7=0\; \; -\; \; ploskost\; \; \to \; \; \vec{n}_{\pi }=(3,-2,5)=\vec{s}_3\\\\ l_3:\; \; \frac{x-1}{3}=\frac{y+1}{-2}=\frac{z+3}{5}$

$2)\; \; l_1:\; \frac{x-1}{2}=\frac{y-3}{3}=\frac{z}{4} \; ,\; \; \; l_2:\; \frac{x+2}{3}=\frac{y+1}{5}=\frac{z-1}{-2} \\\\\vec{s}_1=(2,3,4)\; ,\; \; \vec{s}_2=(3,5,-2)\; ,\; \; M_1(1,3,0)\; ,\; \; M_2(-2,-1,1)\\\\\overline {M_1M_2}=(-3,-4,1)\\\\(\vec{s}_1\cdot \vec{s}_2\cdot \overline {M_1M_2})= \left|\begin{array}{ccc}2&3&4\\3&5&-2\\-3&-4&1\end{array}\right| =2\cdot (5-8)-3\cdot (3-6)+\\\\\\+4\cdot (-12+15)=-6+9+12=15\ne 0\; \; \Rightarrow \\\\ l_1,\; l_2\notin odnoj\; \; ploskosti\\\\l_1,\; l_2\; -\; skreshivautsya$

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