Can someone explain to me what this means (figure at the end of the post; original link to image: http://imgur.com/7vvDs). I understand the part that says the scalar projection of vector $u$ onto vector $v$ is $|u|\cos(\theta)$.
But I don't understand what the vector projection means. Why is the dot product of $v$ and $u$ divided by the magnitude of $v$ squared? Why does that give us the vector projection?