Question

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

Answer 1

For a line making angles $\alpha ,\beta ,\gamma$ with $x,y\text{and}z$ axes respectively, the direction cosines of the line are $\cos \alpha ,\cos \beta ,\cos \gamma$ respectively.
$\text{Here,}\alpha ={90}^{\circ },\beta ={135}^{\circ },\gamma ={45}^{\circ }\therefore \cos \alpha =0\cos \beta =\frac{-1}{\sqrt{2}}\cos \gamma =\frac{1}{\sqrt{2}}$
So, the dc's of the line are $(0,\frac{-1}{\sqrt{2}},\frac{1}{\sqrt{2}})$