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Q.

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors a→,b→ and c→ respectively. Then choose the correct relation for these vectors.

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a

b→=a→−2(a→ . c→)c→

b

b→=a→−c→

c

b→=2a→+c→

d

b→=a→+2c→

answer is A.

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Detailed Solution

QS→=QR→+RS→⇒(QS)b→=(QR)a→+(RS)c→⇒b^=a^+RSQS⋅c^⇒b→=a→+2STQS⋅c→⇒b→=a→+2cos⁡θ⋅c→⇒b→=a→−2cos⁡(π−θ)⋅c→⇒b→=a→−2(a→⋅c→)c→
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