Question

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

Answer 1

$l:; ; left { {{2x+y+z-2=0} atop {2x+2y-z+4=0}} right. ; ; to ; ; vec{n}_1=(2,1,1); ,; ; vec{n_2}=(2,2,-1)\\\vec{n}_1times vec{n}_2=left|begin{array}{ccc}i&j&k\2&1&1\2&2&-1end{array}right|=i(-1-2)-j(-2-2)+k(4-2)=-3i+4j+2k\\\vec{s}=(3,-4,-2)$

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