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

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (C)

$2$

Answer 2

$cos^{2}\,\alpha+cos^{2}\,\beta+cos^{2}\,\gamma=1$ $\left(1-sin^{2}\,\alpha\right)+\left(1-sin^{2}\beta\right)+\left(1-sin^{2}\gamma\right)=1$ or $sin^{2}\alpha+sin^{2}\beta+sin^{2}\gamma=3-1=2$