JEE Main 2022 (Online) 29th June Morning ShiftQuestion 1
If the mirror image of the point $(2,4,7)$ in the plane $3x-y+4z=2$ is $(a,b,c)$, then $2a+b+2c$ is equal to :
3D Geometry
Solution
Normal $(3,-1,4)$; $3(2)-4+28-2=28$, $|n|^2=26$. Image $=(2,4,7)-\frac{2\cdot28}{26}(3,-1,4)=\left(-\tfrac{58}{13},\tfrac{80}{13},-\tfrac{21}{13}\right)$. $2a+b+2c=\frac{-116+80-42}{13}=-6$. Option (C).