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?

Printable View

- May 2nd 2009, 01:22 PMlord12why 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? - May 2nd 2009, 03:29 PMDeadstar
edited for stupidity

- May 2nd 2009, 04:02 PMGamma
Good question man, I don't see how orthogonality plays any role.

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

$\displaystyle ||u||^2+u\cdot v + v\cdot u +||v||^2 + ||u||^2-u\cdot v - v\cdot u +||v||^2 = 2||u||^2+2||v||^2$