A vector $\overrightarrow{r}$ is inclined at equal angles to$OX,$$OY and OZ.$If the magnitude of $\overrightarrow{r}$is $6$ units ,

then $\overrightarrow{r}$=

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

equally inclined to the coordinate axes. Then,

$\therefore l=m=n=\pm \frac{1}{\sqrt{3}}$

Hence, $\overrightarrow{r}=\left|\stackrel{ }{\overrightarrow{r}}\right|(l\widehat{i}+m\widehat{j}+n\widehat{k})$

$\Rightarrow \overrightarrow{r}=6\left\{\pm \frac{1}{\sqrt{3}}\widehat{i}\pm \frac{1}{\sqrt{3}}\widehat{j}\pm \frac{1}{\sqrt{3}}\widehat{k}\right\}=2\sqrt{3}(\pm \widehat{i}\pm \widehat{j}\pm \widehat{k})$