Question

If a line makes angles ${90}^o$ and ${60}^o$ respectively with the positive directions of $x$ and $y$ axes, find the angle which it makes with the positive direction of $z-$axis.

Answer 1

We know that

$l^2+m^2+n^2=1$ where $l,m,n$ are direction cosines

${\cos }^2{90}^{\circ }+{\cos }^2{60}^{\circ }+{\cos }^2\theta =1$

$\frac{1}{4}+{\cos }^2\theta =1$

$\cos \theta =\pm \frac{\sqrt{3}}{2}$

$\theta ={30}^{\circ }$

It makes ${30}^{\circ }$ with positive z-axis.