Question

Find the direction cosines of $x,yandz-axis$.

Answer 1

Direction cosines of the line making an angle $\alpha ,\beta ,\text{and}\gamma \text{with}x,y\text{and}z-\text{axis are}l,m,n$.

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

$x-\text{axis makes an angle of}{0}^{\circ },{90}^{\circ },{90}^{\circ }$
$\text{respectively with}x,y\text{and}z-\text{axis}$

Direction cosines are : $\cos 0^{\circ },\cos {90}^{\circ },\cos {90}^{\circ }$
Direction cosines are : $1,0,0$

$y\text{axis makes an angle of}{90}^{\circ },0^{\circ },{90}^{\circ }$
$\text{respectively with}x,y\text{and}z-\text{axis}$

Direction cosines are : $\cos {90}^{\circ },\cos 0^{\circ },\cos {90}^{\circ }$
Direction cosines are : $0,1,0$

$z-\text{axis makes an angle of}{90}^{\circ },{90}^{\circ },0^{\circ }$
$\text{respectively with}x,y\text{and}z-\text{axis}$

Direction cosines are : $\cos {90}^{\circ },\cos {90}^{\circ },\cos 0^{\circ }$
Direction cosines are : $0,0,1$

Hence, the direction cosines of $x,y\text{and}z-\text{axis}$ are $(1,0,0),(0,1,0)\text{and}(0,0,1)$ respectively.