How do I find the orthogonal vector projection of vec{a} onto vec{b}?

The orthogonal projection of $\vec{a}$ onto $\vec{b}$ can be found by
$\left(\vec{a} \cdot \frac{\vec{b}}{| \vec{b} |}\right) \frac{\vec{b}}{| \vec{b} |} = \frac{\vec{a} \cdot \vec{b}}{| \vec{b} {|}^{2}} \vec{b}$