Let position vectors of the vertices A, B, C and D of the parallelogram ABCD with respect to O be , , and respectively.

⇒

Also, let us assume position vector of P is .

Given ABCD is a parallelogram.

We know that the two diagonals of a parallelogram bisect each other. So, P is the midpoint of AC and BD.

As P is the midpoint of AC, using midpoint formula, we have

P is also the midpoint of BC.

So,

Now we have and.

Adding these two equations, we get

Thus.