Q118 / 170 · Manipal (MET) 2021 · Mathematics

If $\alpha, \beta, \gamma$ are the angles which a half ray makes with the positive direction of the axes, then $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma$ is equal to

  • A
    1
  • Correct answer
    B
    2
  • C
    0
  • D
    -1

Solution

Since, a ray makes angles $\alpha, \beta, \gamma$ with the positive direction of the axes. $\begin{array}{lr}\therefore & \cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1 \\ \Rightarrow & 1-\sin ^2 \alpha+1-\sin ^2 \beta+1-\sin ^2 \gamma=1 \\ \Rightarrow & \sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=2\end{array}$

Hence, the correct answer is option: 'B'.

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