The direction cosines of a line which makes equal angles with co-ordinate axes are:

$±\left(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right)$

The correct answer is Option (1) → $±\left(\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}},\frac{1}{\sqrt{3}}\right)$

For a line making equal angles with all coordinate axes:

Let the direction cosines be $(l, m, n)$.

Since it makes equal angles, $l = m = n$.

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

$3l^2 = 1 \Rightarrow l = \pm \frac{1}{\sqrt{3}}$

Hence direction cosines:

$\left(\pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}, \pm \frac{1}{\sqrt{3}}\right)$

Correct answer: $\pm\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right)$