Question

A straight line which makes an angle of ${60}^o$ with each of y and z-axes, this line makes with x-axis an angle :

• A. ${30}^o$
• B. ${60}^o$
• C. ${75}^o$
• D. ${45}^o$

Answer 1

The correct option is D ${45}^o$

Clearly, ${\cos }^2\alpha +{\cos }^2{60}^o+{\cos }^2{60}^o=1$ , where $\alpha$ is the angle which the straight line makes with x-axis,
$\therefore {\cos }^2\alpha =1-\frac{1}{4}-\frac{1}{4}=\frac{1}{2}$
$\Rightarrow \cos \alpha =\frac{1}{\sqrt{2}}\Rightarrow \alpha ={45}^o$