JEE Main 2020 (Online) 2nd September Morning ShiftQuestion 1
The plane passing through the points $(1,2,1)$, $(2,1,2)$ and parallel to the line, $2x=3y$, $z=1$ also passes through the point :
3D Geometry
Solution
Line $2x=3y,\ z=1$ has direction $(3,2,0)$. Plane through $(1,2,1)$ with direction $(1,-1,1)$ (between the points) and $(3,2,0)$: normal $=(1,-1,1)\times(3,2,0)=(-2,3,5)$. Plane: $-2(x-1)+3(y-2)+5(z-1)=0\Rightarrow -2x+3y+5z=9$. Test $(-2,0,1)$: $4+0+5=9$ yes. Option (B).