Question

If a line makes angle ${90}^{\circ },{60}^{\circ }$ and ${30}^{\circ }$ with the positive direction of $x,y$ and $z-axis$ respectively, find its direction cosines.

Answer 1

Direction cosines are given by:
$l=\cos \alpha =\cos {90}^{\circ }$
$\therefore l=0$
$m=\cos \beta =\cos {60}^{\circ }$
$\therefore m=\frac{1}{2}$
$n=\cos \gamma =\cos {30}^{\circ }$
$\therefore n=\frac{\sqrt{3}}{2}$
$\therefore l,m,n=0,\frac{1}{2},\frac{\sqrt{3}}{2}$ are the direction cosines.