If the direction cosines of a line are $\left< \frac{1}{c}, \frac{1}{c}, \frac{1}{c} \right>$, then

$c = \pm\sqrt{3}$

The correct answer is Option (4) → $c = \pm\sqrt{3}$ ##

We know,

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

$\Rightarrow \left( \frac{1}{c} \right)^2 + \left( \frac{1}{c} \right)^2 + \left( \frac{1}{c} \right)^2 = 1$

$\Rightarrow 3 \left( \frac{1}{c} \right)^2 = 1$

$\Rightarrow c = \pm\sqrt{3}$