JEE Main 2020 (Online) 8th January Evening ShiftQuestion 1
The mirror image of the point $(1,2,3)$ in a plane is $\left(-\frac73,-\frac43,-\frac13\right)$. Which of the following points lies on this plane ?
3D Geometry
Solution
Plane is the perpendicular bisector of the segment. Normal $=B-A=(-\tfrac{10}3,-\tfrac{10}3,-\tfrac{10}3)\parallel(1,1,1)$. Midpoint $=(-\tfrac13,\tfrac13,\tfrac43)$, coordinate sum $=1$, so plane: $x+y+z=1$. Check: $(1,-1,1)$: $1$ yes. Others: $-3,3,-1$ no. Option (C).