Question

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

Answer 1

Let direction cosines of the line be l,m and n with the X,Y, and Z-axes respectively and given that

$\alpha ={90}^{\circ },\beta ={135}^{\circ }and\gamma ={45}^{\circ }Then,l=cos\alpha =cos{90}^{\circ }=0,m=cos\beta =cos{135}^{\circ }=-1/\sqrt{2}andn=cos\gamma =cos{45}^{\circ }=1/\sqrt{2}$

Therefore, the direction cosines of the line are $0,-\frac{1}{\sqrt{2}}and\frac{1}{\sqrt{2}}$