Question

The direction cosines of a line which is equally inclined to axes, is given by

• A. $\pm \frac{1}{3}$
• B. $\pm \frac{1}{\sqrt{3}}$
• C. $1$
• D. $0$

Answer 1

The correct option is B $\pm \frac{1}{\sqrt{3}}$

Consider the problem

Let, $l=m=n=\cos \alpha$

then,

$l^2+m^2+n^2={\cos }^2\alpha +{\cos }^2\alpha +{\cos }^2\alpha$

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

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

$\cos \alpha =\pm \frac{1}{\sqrt{3}}$

thus,

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