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!!
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?