Question

If a line makes angles ${90}^o,{135}^o,{45}^o$ with x, y and z-axis respectively, find its direction cosines.

Answer 1

Let direction cosines of the line be l, m and 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 $0,\frac{-1}{\sqrt{2}},\frac{1}{\sqrt{2}}$.