If a vector $\vec{A}$ makes an angles $\alpha, \beta$ and $\gamma$ respectively with the $x, y$ and

Question

If a vector $\vec{A}$ makes an angles $\alpha, \beta$ and $\gamma$ respectively with the $x, y$ and $z$ axes respectively. Then $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma$ is equal to

Professor PC Thomas Classes · Answer

(c) : $\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma=1$ $\left(1-\sin ^2 \alpha\right)+\left(1-\sin ^2 \beta\right)+\left(1-\sin ^2 \gamma\right)=1$ or $\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma=3-1=2$