Question

Find the direction cosines of the line which is equally inclined with the co-ordinates axes.

Answer 1

let the angle subtended with each of the coordinate axis be Q

then

$l=m=n=\cos \theta$

$l^2=m^2=n^2=1$

${\cos }^2\theta +{\cos }^2\theta +{\cos }^2\theta =1$

$3{\cos }^2\theta =1$

${\cos }^2=\frac{1}{3}$

$\cos {\theta }^{}=\pm \frac{1}{\sqrt{3}}$

therefore l = m = n = $\pm \frac{1}{\sqrt{3}}$