JEE Main 2019 (Online) 12th April Evening ShiftQuestion 1
The length of the perpendicular drawn from the point $(2,1,4)$ to the plane containing the lines $\vec r=(\hat i+\hat j)+\lambda(\hat i+2\hat j-\hat k)$ and $\vec r=(\hat i+\hat j)+\mu(-\hat i+\hat j-2\hat k)$ is
3D Geometry
Solution
Normal $=(1,2,-1)\times(-1,1,-2)=(-3,3,3)$; plane $-x+y+z=0$ through $(1,1,0)$. Distance of $(2,1,4)$: $\frac3{\sqrt3}=\sqrt3$.