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

Explanation

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

### Step 1: Define the Vectors
Let the vertices of the parallelogram be \( O, A, B, C \). We define the vectors:
- \( \vec{OA} = \vec{A} \)
- \( \vec{OB} = \vec{B} \)

### Step 2: Use the Given Condition
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