If two vectors u and v fit the equation (u - v) times (u - v) = u times u + v times v, how must these vectors u and v be related? What familiar theorem does this equation represent?
$\displaystyle \left( {u - v} \right) \cdot \left( {u - v} \right) = u \cdot u - 2u \cdot v + v \cdot v$
but if that is $\displaystyle u \cdot u - 2u \cdot v + v \cdot v = u \cdot u + v \cdot v$
do you see that $\displaystyle 2u \cdot v = 0$?
So what does that mean about u & v?