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Thread: Scalar product

  1. #1
    Junior Member
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    Scalar product

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

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

    Thanks in advance!
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  2. #2
    MHF Contributor
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    Re: Scalar product

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

    $u \perp v \Rightarrow u \cdot v = 0$

    $|u+v|^2 = u\cdot u + v\cdot v = |u|^2 + |v|^2$
    Thanks from HallsofIvy, Isa16 and topsquark
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