Projection of a vector I am reading some material on the Householder reflection and it describes the projection of a vector $\vec{x}$, onto $\vec{v}$ in vector notation to be:
$\frac{\vec{x}\cdot \vec{v}}{||\vec{v}||^2}\vec{v}$ 
Where $a\cdot b$ is the dot product of vectors a and b. 
So how is that? 
I know if θ is the angle between $\vec{x}$ and $\vec{v}$, then in trigonometric terms, the projection of $\vec{x}$ on $\vec{v}$ would be $x\cos(θ)$. How are these two equivalent? Thanks.

Firstly your equation is slightly off. I'll derive the correct equation directly to show you why.
Recall that $x\cdot v = |x||v|\cos(\theta)$
$$\frac{x\cdot v}{v\cdot v}v=\frac{|x||v|\cos(\theta)}{|v|^2}v=|x|\cos(\theta)\frac{v}{|v|}$$
So this vector has length $|x|\cos(\theta)$ and it points in the direction of $v$, which is precisely what the trig should tell you.
