Hi,can someone please explain how to solve this question to me.

1) For any two vectors u and v, prove that |u + v|^2 + |u -v|^2 = 2(|u|^2 + |v|^2)

In proving this, what geometric fact have your proved?

Thanks heaps!!

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- Mar 13th 2013, 05:20 PMVishakVectors proof question
Hi,can someone please explain how to solve this question to me.

1) For any two vectors u and v, prove that |u + v|^2 + |u -v|^2 = 2(|u|^2 + |v|^2)

In proving this, what geometric fact have your proved?

Thanks heaps!! - Mar 13th 2013, 05:26 PMILikeSerenaRe: Vectors proof question
- Mar 13th 2013, 05:45 PMVishakRe: Vectors proof question
I'm not sure what the triangle brackets mean, but ill guess - is it just u^2 + 2uv + v^2?

- Mar 13th 2013, 05:45 PMPlatoRe: Vectors proof question
- Mar 13th 2013, 10:20 PMVishakRe: Vectors proof question
Thanks guys, what about the second part - "what geometric fact have you proved?"

- Mar 14th 2013, 02:51 AMILikeSerenaRe: Vectors proof question
The triangle brackets are one of the ways you can write a dot product of vectors.

You can also write it as $\displaystyle (u+v) \cdot (u+v)$.

And yes, that is what it is.

Care to guess now that you know that $\displaystyle u~\&~v$ are adjacent sides of a parallelogram and $\displaystyle (u+v)~\&~(u-v)$ are its diagonals?