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Question: If vector \(\alpha , \beta\) and \(\gamma\)respectively with the x, y and z axes respectively. Then ...

If vector α,β\alpha , \beta and γ\gammarespectively with the x, y and z axes respectively. Then sin⁡2α+sin⁡2β+sin⁡2γ\sin ^ { 2 } \alpha + \sin ^ { 2 } \beta + \sin ^ { 2 } \gammais equal to

A

0

B

1

C

2

D

3

Answer

2

Explanation

Solution

cos⁡2α+cos⁡2β+cos⁡2γ=1\cos ^ { 2 } \alpha + \cos ^ { 2 } \beta + \cos ^ { 2 } \gamma = 1

(1−sin⁡2α)+(1−sin⁡2β)+(1−sin⁡2γ)=1\left( 1 - \sin ^ { 2 } \alpha \right) + \left( 1 - \sin ^ { 2 } \beta \right) + \left( 1 - \sin ^ { 2 } \gamma \right) = 1

Or sin⁡2α+sin⁡2β+sin⁡2γ=3−1=2\sin ^ { 2 } \alpha + \sin ^ { 2 } \beta + \sin ^ { 2 } \gamma = 3 - 1 = 2