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Question: If \(\alpha , \beta , \gamma\) be the angles which a line makes with the positive direction of co-o...

If α,β,γ\alpha , \beta , \gamma be the angles which a line makes with the positive direction of co-ordinate axes, then sin⁡2α+sin⁡2β+sin⁡2γ=\sin ^ { 2 } \alpha + \sin ^ { 2 } \beta + \sin ^ { 2 } \gamma =

A

2

B

1

C

3

D

0

Answer

2

Explanation

Solution

Since cos⁡2α+cos⁡2β+cos⁡2γ=1\cos ^ { 2 } \alpha + \cos ^ { 2 } \beta + \cos ^ { 2 } \gamma = 1 ⇒Σsin⁡2α=3−1=2\Rightarrow \Sigma \sin ^ { 2 } \alpha = 3 - 1 = 2.