The direction cosines of a line which makes equal angles with the co-ordinate axes are____

Let $\left(l, m, n\right) = \left(\cos \alpha , \cos \beta , \cos \gamma \right)$

are direction cosines.

We know that $\left(l, m, n\right)$ are direction cosines then $\Rightarrow l^2+m^2+n^2=1$

Given that they are making equal angles with axes

$i.e \cos \alpha = \cos \beta = \cos \gamma$

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

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

So Required is $\left(\frac{\pm 1}{\sqrt{3}}, \frac{\pm 1}{\sqrt{3}}, \frac{\pm 1}{\sqrt{3}}\right)$.