Using dot product of vectors, prove that a parallelogram, whose diagonals are equal, is a rectangle

Explanation

To prove that a parallelogram whose diagonals are equal is a rectangle using the dot product of vectors, we can follow these steps:

### Step 1: Define the vectors
Let \( O \) be the origin, and let \( A \) and \( B \) be the points such that:
- \( \vec{OA} = \vec{a} \)
- \( \vec{OB} = \vec{b} \)

The points \( C \) and \( D \) can be defined as:
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