What is the value of $<u,v>^2$?

Question

Let $V$ be an inner product space. What is the value of $<u,v>^2 = <u,v> <u,v> $?

where $u, v \in V$ and $<,>$ is the inner product on $V$.

Thanks for your help.

Answer 1

If $\alpha$ is the angle between $u$ and $v$ then

$<u,v>^2=||u||^2*||v||^2*\cos^2(\alpha)$