# Thread: proof that 2 vectors of same length are perpindicular if subtracted

1. ## proof that 2 vectors of same length are perpindicular if subtracted

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|
$\vec u \cdot \vec v = |u|^2$
$(u_1)(v_1)+(u_2)(v_2)...(u_n)(v_n) = |u|^2$
and I have no clue

2. 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.