Answer
Along direction of $v$: $\frac{1}{5\sqrt{2}}(4\mathbf{i}-5\mathbf{j}+3\mathbf{k})$
Opposite direction of $v$: $-\frac{1}{5\sqrt{2}}(4\mathbf{i}-5\mathbf{j}+3\mathbf{k})$
Work Step by Step
$\mathbf{v}=4\mathbf{i}-5\mathbf{j}+3\mathbf{k}$
$\|\mathbf{v}\|=\sqrt{16+25+9}=\sqrt{50}=5\sqrt{2}$
Unit vector in the direction of $\mathbf{v}$: $\frac{1}{5\sqrt{2}}(4\mathbf{i}-5\mathbf{j}+3\mathbf{k})$
Unit vector in the opposite direction of $\mathbf{v}$: $-\frac{1}{5\sqrt{2}}(4\mathbf{i}-5\mathbf{j}+3\mathbf{k})$
