You need to show that (u+v).(u-v)=0
Expand, cancel middle terms, remember that u.u = u^2 (same for v), and you've got it.
show that if u and v are any 2 vectors of the same length that u+v and u-v are perpendicular. Give a coordinate free proof using the dot product that holds true in n-space.
So I started like this:
|u|=|v|
and I have no clue