JEE Main 2021 (Online) 26th February Evening ShiftQuestion 1
If the mirror image of the point $(1,3,5)$ with respect to the plane $4x-5y+2z=8$ is $(\alpha,\beta,\gamma)$, then $5(\alpha+\beta+\gamma)$ equals :
3D Geometry
Solution
$4-15+10-8=-9$, $|n|^2=45$. Image $=P+\frac{18}{45}(4,-5,2)=(\frac{13}5,1,\frac{29}5)$, sum $=\frac{47}5$, so $5\times$ sum $=47$.