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Math Help - why is this false?

  1. #1
    Junior Member
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    why is this false?

    Two vectors u, v are orthogonal if and only if ||u+v||^2 +||u-v||^2 = 2||u||^2 - 2||v||^2?


    Doesn't (u+v)(u+v) + (u-v)(u-v) = u^2 + v^2?
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  2. #2
    Super Member Deadstar's Avatar
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    edited for stupidity
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  3. #3
    Super Member Gamma's Avatar
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    Good question man, I don't see how orthogonality plays any role.
    ||u+v||^2+ ||u-v||^2=(u+v)\cdot(u+v)+(u-v)\cdot(u-v)
    ||u||^2+u\cdot v + v\cdot u +||v||^2 + ||u||^2-u\cdot v - v\cdot u +||v||^2 = 2||u||^2+2||v||^2
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