(1) Realize that if A & B are vectors that are adjacent sides of a parallelogram then (A+B) and (A-B) are the diagonals. We know . Recalling what equilateral means the result follows at once.
(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 where both of these vectors give the diagonals?
(2) Prove the law of sines using the cross product.
So we want to prove that
So gives the area of a parallelogram formed by . How would I proceed from here?