JEE Main 2021 (Online) 31st August Evening ShiftQuestion 1
The distance of the point $(-1,2,-2)$ from the line of intersection of the planes $2x+3y+2z=0$ and $x-2y+z=0$ is :
3D Geometry
Solution
Line passes through origin with direction $(2,3,2)\times(1,-2,1)=(7,0,-7)\parallel(1,0,-1)$. For $(-1,2,-2)$: $|v|^2=9$, $v\cdot d=1$, $|d|^2=2$, distance$^2=9-\frac12=\frac{17}2$, distance $=\frac{\sqrt{34}}2$.