(1)Prove that the diagonals of an equilateral parallelogram are perpendicular.

So this is basically a square right? Is this essentially the same thing as $\displaystyle (A-B) \cdot (A+B) = 0$ where both of these vectors give the diagonals?

(2)Prove the law of sines using the cross product.

So we want to prove that $\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} $

So $\displaystyle A \times B = |A||B| \sin \theta $ gives the area of a parallelogram formed by $\displaystyle A,B,C $. How would I proceed from here?