Cauchy-Schwarz inequality with zero angle? 
Cauchy-Schwarz Inequality:
If $\textbf{u}$ and $\textbf{v}$ are vectors in a real inner product space $V$, then $$|\left\langle\textbf{u},\textbf{v}\right\rangle|\leq||\textbf{u}||\ ||\textbf{v}||$$

What will happen with the Cauchy-Schwarz inequality if the angle between the two vectors is zero?

the definition of the angle $\alpha\in[0,\pi]$ between $u,v$ is:
$$
\cos\alpha = \frac{\langle u,v\rangle}{\|u\| \|v\|}
$$
so  $\alpha =0 $ iff
$$
1=\frac{\langle u,v\rangle}{\|u\| \|v\|}\iff
\langle u,v\rangle = \|u\| \|v\|
$$
