If the direction cosines of a line are $k$, $k$ and $k$, then

$k = \frac{1}{\sqrt{3}}$ or $-\frac{1}{\sqrt{3}}$

The correct answer is Option (4) → $k = \frac{1}{\sqrt{3}}$ or $-\frac{1}{\sqrt{3}}$ ##

Since, direction cosines of a line are $k, k$ and $k$.

$∴l = k, m = k \text{ and } n = k$

We know that, $l^2 + m^2 + n^2 = 1$

$\Rightarrow k^2 + k^2 + k^2 = 1 \Rightarrow 3k^2 = 1 \Rightarrow k^2 = \frac{1}{3}$

$∴k = \pm \frac{1}{\sqrt{3}}$