Proving the parallelogram law with diagonal and side norms

[TiberiusK]

Consider the parallelogram
with adjacent sides OP; OQ where P is the point (x1; x2); Q is the point (y1; y2) and O is
the origin.What does this $$||x + y||^{2}+ ||x - y||^{2} = 2(||x||^{2} + ||y||^2)$$say about a parallelogram in the plane?
I know $$||x + y|| & ||x -y||$$ represent the diagonals but is there any way of proving it?

 

[tiny-tim]

Hi TiberiusK!

I think all the question is asking is, how would you write in ordinary English the meaning of that equation?