Answer
$\frac{2}{\sqrt{6}}i-\frac{1}{\sqrt{6}}j+\frac{1}{\sqrt{6}}k.$
Work Step by Step
If $v=ai+bj+ck$ and $||v||=\sqrt{a^2+b^2+c^2}$, then the unit vector $u$ in the same direction as $v$ is
$u=\frac{v}{||v||}$.
The magnitude of $v$ is
$||v||=\sqrt{2^2+(-1)^2+1^2}\\||v||=\sqrt{4+1+1}=\sqrt{6}.$
Thus the unit vector is:
$u=\frac{2i-j+j+k}{\sqrt{6}}=\\u=\frac{2}{\sqrt{6}}i-\frac{1}{\sqrt{6}}j+\frac{1}{\sqrt{6}}k.$
