The vector projection of $\bfx$ onto $\bfv$ is the vector given by the multiple of $\bfv$ obtained by dropping down a perpendicular line from $\bfx$.
The vector projection of $\bfx$ onto $\bfv$ is the point closest to $\bfx$ on the line given by all multiples of $\bfv$.
The vector projection of $\bfx$ onto $\bfv$ is $$\text{proj}_{\bfv}\ \bfx = (\bfx\cdot \bfv) \frac{\bfv}{\left| \bfv \right|^2}.$$
If $\theta$ is the angle between $\bfx$ and $\bfv$, the vector projection $\text{proj}_\bfv \bfx$ is the vector of length $\left| \bfx \right| \cos \theta$ that is in the direction of $\bfv$.
