Given:

$\displaystyle \vec{u}\bullet\vec{v}$ = $\displaystyle |\vec{u}||\vec{v}|\cos{\theta}$

Prove that $\displaystyle |\vec{u}\bullet\vec{v}| \leq |\vec{u}||\vec{v}|$

I have:

$\displaystyle \vec{u}\bullet\vec{v}$ = $\displaystyle |\vec{u}||\vec{v}|\cos{\theta}\leq|\vec{u}||\vec{v }| (1)$ since $\displaystyle |\cos{\theta}|\leq1$

How do I jump from that to $\displaystyle |\vec{u}\bullet\vec{v}| \leq |\vec{u}||\vec{v}|$. I realize it's probably very simple. If someone could just help me take the leap I would appreciate it!

I guess I know that the dot product is a scalar so I'm wondering..I don't know...geez louise.

P.S. It's like 1 in the morning, and this is my last quesiton