Question

If a line makes angles ${90}^{\circ },{60}^{\circ }$ and ${30}^{\circ }$ with the positive direction of $x,y$ and z-axes respectively, find its direction cosines

Answer 1

Let the angles made by the line with positive x axis, y axis and z axis be $\alpha ,\beta ,\gamma$ then

$\alpha ={90}^0$, $\beta ={60}^0$ and $\gamma ={30}^0$.

Therefore the direction cosines of the lines are

$(cos\alpha ,cos\beta ,cos\gamma )$

$=(0,\frac{1}{2},\frac{\sqrt{3}}{2})$