Question

If a line OP through the origin O makes angles of ${30}^o$,${45}^{\circ }$ and ${60}^{\circ }$ with $x,yandz$ axis respectively then the direction cosines of OP are

Answer 1

Given line OP makes an angles of ${30}^o,{45}^o$ and ${60}^o$

with $x,y$ and $z-axis$ respectively

Then direction cosines of a line making angle $\alpha$ with

$X-axis$ ,$\beta$ with $y-axis$ and $y$ with $z-axis$ are $l,m,n$

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

$l=\cos {30}^o$ ,$m=\cos {45}^o$ , $n=\cos {60}^o$

$l=\frac{\sqrt{3}}{2}$ , $m=\frac{1}{\sqrt{2}}$, $n=\frac{\sqrt{3}}{2}$