`A B C D` is parallelogram and `P` is the point of intersection of its diagonals. If `O` is the origin of reference, show that ` vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot`

Explanation

To prove that \( \vec{OA} + \vec{OB} + \vec{OC} + \vec{OD} = 4 \vec{OP} \) for a parallelogram ABCD with point P as the intersection of its diagonals, we can follow these steps:

### Step 1: Define the vectors
Let:
- \( \vec{O} \) be the origin,
- \( \vec{A} \), \( \vec{B} \), \( \vec{C} \), and \( \vec{D} \) be the position vectors of points A, B, C, and D respectively.

### Step 2: Express the position vectors of the points
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