Question

If a line makes angles ${90}^{\circ },{135}^{\circ },{45}^{\circ }$ with the $x,y$ and $Z-\text{axes}$ respectively, find its direction cosines.

Answer 1

Let the direction cosines of the line be $l,m,n$.
$l=\cos {90}^o=0$
$m=\cos {135}^o=-\frac{1}{\sqrt{2}}$
$n=\cos {45}^o=\frac{1}{\sqrt{2}}$
Therefore, the direction cosines of the line are $0,-\frac{1}{\sqrt{2}}$ and $\frac{1}{\sqrt{2}}$.