Question 13 of 295

The incident ray, reflected ray and the outward drawn normal are denoted by the unitvectors $\vec{a},\vec{b}$and $\vec{c}$ respectively. Then choose the correct relation for these vectors.

A$\vec{b}=\vec{a}+2\vec{c}$B$\vec{b}=2\vec{a}+\vec{c}$C$\vec{b}=\vec{a}-2\left(\vec{a}\cdot \vec{c}\right)\vec{c}$D$\vec{b}=\vec{a}-\vec{c}$

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Answer: (C) $\vec{b}=\vec{a}-2\left(\vec{a}\cdot \vec{c}\right)\vec{c}$

$\vec{a}=\sin \theta \hat{i}-\cos \theta \hat{j}$
$\vec{b}=\sin \theta \hat{i}+\cos \theta \hat{j}$
$\vec{c}=\hat{j}$
$\vec{a}-2\left(\vec{a}\cdot \vec{c}\right)\vec{c}=\sin \theta \hat{i}+\cos \theta \hat{j}$