A vector $\vec{r}$ is equally inclined to coordinate axes and its magnitude is 6 units, then $\vec{r}$ is ________.

$2\sqrt{3}(±\hat{i}±\hat{j}±\hat{k})$

The correct answer is Option (1) → $2\sqrt{3}(±\hat{i}±\hat{j}±\hat{k})$

let $\vec v=a\hat i+a\hat j+a\hat k$

$|\vec v|=|\sqrt{3}a|=6$

so $a=±2\sqrt{3}$

$\vec v=2\sqrt{3}(±\hat i±\hat j±\hat k)$