Hello, I am stuck on a problem that at the conceptual level makes perfect sense. Here's the problem:
Use vectors to show that the diagonals of a parallelogram have the same length if and only if the parallelogram is a rectangle. (Hint: let a and b be vectors along two sides of the parallelogram. Express vectors running along the diagonals in terms of a and b.)
I have attached a picture. I can let:
d1 = a + b
d2 = b - a
I know that I am trying to prove that:
When for the angle between a and b.
Most of my work so far essentially amounts to me plugging in for the Angle Between Two Vectors formula and coming out with a dotted with b = 0. This occurs if either is the 0 vector or if they are perpendicular. However, this doesn't help me with the length of d1 and d2. I am not sure how I can relate the two together. Thanks for any assistance.