Q 12-09-165JEE MainJEE Main 2021 (26 Feb, Shift 2)Medium
The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ respectively. Then choose the correct relation for these vectors.
Answer: (C) $\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}$
On reflection, the component of the ray parallel to the surface is unchanged and the component along the normal is reversed.
The normal component of $\vec{a}$ is $(\vec{a}\cdot\vec{c})\vec{c}$, so
$$\vec{b} = \vec{a} - 2(\vec{a}\cdot\vec{c})\vec{c}$$
Solution by Sreeraj P, M.Sc Physics