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? Thanks in advance!
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$|u+v|^2 = (u+v)\cdot(u+v) = u\cdot u + 2 u\cdot v + v\cdot v$ $u \perp v \Rightarrow u \cdot v = 0$ $|u+v|^2 = u\cdot u + v\cdot v = |u|^2 + |v|^2$