Question

Написать канонические уравнения прямой.
2x+y+z-2=0 , 2x + 2y-z+4=0

Answer 1

$l:\; \; \left \{ {{2x+y+z-2=0} \atop {2x+2y-z+4=0}} \right. \; \; \to \; \; \vec{n}_1=(2,1,1)\; ,\; \; \vec{n_2}=(2,2,-1)\\\\\\\vec{n}_1\times \vec{n}_2=\left|\begin{array}{ccc}i&j&k\\2&1&1\\2&2&-1\end{array}\right|=i(-1-2)-j(-2-2)+k(4-2)=-3i+4j+2k\\\\\\\vec{s}=(3,-4,-2)$

$x=1\; \; \to \; \; \left \{ {{y+z=0} \atop {2y-z=-6}} \right. \; \plus \; \left \{ {{y+z=0} \atop {3y=-6}} \right. \; \; \left \{ {{z=2} \atop {y=-2}} \right. \; \; \Rightarrow \; \; M(1,-2,2)\\\\l:\; \frac{x-1}{3}=\frac{y+2}{-4}=\frac{z-2}{-2}$