JEE MAIN - Physics (2021 - 26th February Evening Shift - No. 9)
The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ respectively. Then choose the correct relation for these vectors.
$$\overrightarrow b $$ = $$\overrightarrow a $$ + 2$$\overrightarrow c $$
$$\overrightarrow b $$ = $$\overrightarrow a $$ $$-$$ 2 ($$\overrightarrow a $$ . $$\overrightarrow c $$)$$\overrightarrow c $$
$$\overrightarrow b $$ = 2$$\overrightarrow a $$ + $$\overrightarrow c $$
$$\overrightarrow b $$ = $$\overrightarrow a $$ $$-$$ $$\overrightarrow c $$
Explanation
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Here $$\overrightarrow a = \left| {\overrightarrow a } \right|\sin \theta \widehat i - \left| {\overrightarrow a } \right|\cos \theta \widehat j$$
As $$\overrightarrow a $$ is an unit vector, so $$\left| {\overrightarrow a } \right|$$ = 1
$$ \therefore $$ $$\overrightarrow a = \left| {\overrightarrow a } \right|\sin \theta \widehat i - \left| {\overrightarrow a } \right|\cos \theta \widehat j$$
= $$ \sin \theta \widehat i - \cos \theta \widehat j$$
Similarly $$\overrightarrow b = \sin \theta \widehat i + \cos \theta \widehat j$$
and $$\overrightarrow c = \widehat j$$
From option (B),
$$\overrightarrow a $$ $$-$$ 2 ($$\overrightarrow a $$ . $$\overrightarrow c $$)$$\overrightarrow c $$
= $$\sin \theta \widehat i + \cos \theta \widehat j$$ = $$\overrightarrow b $$
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