Question

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

Answer 1

$\left[\begin{array}{c}\text{Direction cosines of the line making angle}\\ \alpha ,\beta \text{and}\gamma \text{with}x,y\text{and}z-\text{axis are}l,m,n.\\ l=\cos \alpha ,m=\cos \beta ,n=\cos \gamma \end{array}\right]$

Here, $\alpha ={90}^{\circ },\beta ={60}^{\circ },\gamma ={30}^{\circ }$

Therefore, direction cosines of the line are

$l=\cos {90}^{\circ },m=\cos {60}^{\circ },n=\cos {30}^{\circ }$

$\Rightarrow l=0,m=\frac{1}{2},n=\frac{\sqrt{3}}{2}$

$\therefore \text{Required direction cosines are}0,\frac{1}{2},\frac{\sqrt{3}}{2}$