Suppose that are the two adjacent vectors determining the parallelogram.
The diagonals of the parallelogram are: .
Look at the following.
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.
I am not sure I understand the significance in dotting the diagonals together. The expression shows that the diagonals dotted together equal the length of a squared minus the length of b squared. Thanks for the help so far, I feel like I am missing something that should be very obvious to me.
Luobo...thank you. That is what I was missing. That makes complete sense. I suppose was too tired to think clearly. I was hoping I could get a nudge, and that's what Plato tried, but I guess the roadblock in my mind just wouldn't allow me go past it. Thanks again!