Let position vectors of the vertices A, B, C and D of the parallelogram ABCD with respect to O be \(\vec a,\vec b,\vec c\)and \(\vec d\) and respectively.
Also, let us assume position vector of P is \(\vec p\).
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
Adding these two equations, we get