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[SOLVED] Vector Calculus: Parallelogram Problem

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:

$\displaystyle \|d1\| = \|d2\|$

When $\displaystyle \cos\theta = 0 $ 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.