The projection vector of $\overrightarrow {\rm{a}}$ on $\overrightarrow {\rm{b}}$ is

Projection vector of $\vec a$ on $\vec b$ is given by $= \vec a \cdot \frac{{\vec b}}{{|\vec b|}}\vec b$

$= \left( {\vec a \cdot \frac{{\vec b}}{{|\vec b|}}} \right) \cdot \vec b$