The direction cosines of a vector $\overrightarrow{r}$ which is equally inclined with $OX, OY and OZ,$ are

Let $l,m,n$ be the direction cosines of $\overrightarrow{r}$. since $\overrightarrow{r}$ is 

equally inclined with  $OX, OY and OZ.$

$\therefore l=m=n [\because \alpha =\beta =\gamma \Rightarrow \cos \alpha =\cos \beta =\cos \gamma ]$

Now, $l^2+m^2+n^2=1\Rightarrow 3l^2=1\Rightarrow l=\pm \frac{1}{\sqrt{3}}$

Hence , direction couines of $\overrightarrow{r}$ are $\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}},\pm \frac{1}{\sqrt{3}}$