`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 solve the problem, we need to show that:

\[ \vec{OA} + \vec{OB} + \vec{OC} + \vec{OD} = 4 \vec{OP} \]

where \( O \) is the origin, \( A, B, C, D \) are the vertices of the parallelogram, and \( P \) is the point of intersection of the diagonals.

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