1. ## Scalar product

Show that if u ⊥ v then:
|u +v|² = |u|²+|v|²

Ps: I've tried some paths, but nothing works. Could you please show me the correct one?

$|u+v|^2 = (u+v)\cdot(u+v) = u\cdot u + 2 u\cdot v + v\cdot v$
$u \perp v \Rightarrow u \cdot v = 0$
$|u+v|^2 = u\cdot u + v\cdot v = |u|^2 + |v|^2$