Question

Prove ||u+v||^2 + ||u-v||^2=2||u||^2+2||v||^2

anybody got an idea where I can start? I can't seem to remember the property I can use to simplify ||u+v||^2

Answer 1

start with ||u+v||^2 = <u+v> dot <u+v>

Answer 2

<u+v> dot <u+v> = ??

Answer 3

and then <u-v> dot <u-v> = ??? add the two and you'll get what you trying to show

Answer 4

Oh so just expand the equation. Thank you!

Answer 5

<u+v> dot <u+v> = ||u||^2 + ||v||^2 + 2 u dot v