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|

$\displaystyle \vec u \cdot \vec v = |u|^2$

$\displaystyle (u_1)(v_1)+(u_2)(v_2)...(u_n)(v_n) = |u|^2$

and I have no clue