Answer
Along direction of $v$: $\frac{1}{\sqrt{35}}(5\mathbf{i}+3\mathbf{j}-\mathbf{k})$
Opposite direction of $v$:$-\frac{1}{\sqrt{35}}(5\mathbf{i}+3\mathbf{j}-\mathbf{k})$
Work Step by Step
$\mathbf{v}=5\mathbf{i}+3\mathbf{j}-\mathbf{k}$
$\|\mathbf{v}\|=\sqrt{25+9+1}=\sqrt{35}$
Unit vector in the direction of $\mathbf{v}$: $\frac{1}{\sqrt{35}}(5\mathbf{i}+3\mathbf{j}-\mathbf{k})$
Unit vector in the opposite direction of $\mathbf{v}$: $-\frac{1}{\sqrt{35}}(5\mathbf{i}+3\mathbf{j}-\mathbf{k})$