JEE Main 2020 (Online) 3rd September Morning ShiftQuestion 1
The foot of the perpendicular drawn from the point $(4,2,3)$ to the line joining the points $(1,-2,3)$ and $(1,1,0)$ lies on the plane :
3D Geometry
Solution
Line: $F=(1,-2+3u,3-3u)$, direction $d=(0,3,-3)$. $P-F=(3,4-3u,3u)$; $(P-F)\cdot d=12-9u-9u=0\Rightarrow u=\tfrac23$, so $F=(1,0,1)$. Only $2x+y-z=2+0-1=1$ holds. Answer (D).