Question

If a point $P$ in the space such that $\overline{OP}$ is inclined to $OX$ at $45$ and $OZ$ to $60$ then $\overline{OP}$ inclined to $OY$ is

• A. ${75}^{\circ }$
• B. ${75}^{\circ }\text{or}{105}^{\circ }$
• C. ${60}^{\circ }\text{or}{120}^{\circ }$
• D. None of these

Answer 1

Answer: (C)

${60}^{\circ }\text{or}{120}^{\circ }$

$l=\cos {45}^O=\frac{1}{\sqrt{2}}$ and $m=\cos {60}^O=\frac{1}{2}$
$\Rightarrow n^2=1-\frac{1}{2}-\frac{1}{4}=\frac{1}{4}\Rightarrow n=\pm \frac{1}{2}$
So $\alpha ={60}^O$ or ${120}^O$