Question

A line makes angles ${90}^o,{135}^o$ and ${45}^o$ with positive directions of x-axis, y-axis and z-axis respectively. What are the direction cosines of the line?

Answer 1

If $\alpha ,\beta ,$ and $\gamma$ are the angles made by the line segment with the coordinate axis.

$cos\alpha ,cos\beta$ and $cos\gamma$ are called as the direction cosines and are usually denoted by $l,m$ and $n.$

$l=cos\alpha ,m=cos\beta$ and $n=cos\gamma$

Direction cosines of the line are $\cos {90}^o,\cos {135}^o,\cos {45}^o$

i.e. $\{0,\frac{-1}{\sqrt{2}},\frac{1}{\sqrt{2}}\}$