Given a quadrilateral ABCD, P is a point outside the quadrilateral and

[given]

Or,

………..(i)[as ]

Consider ΔAPB and apply triangle law of vector, we get

And consider ΔDPC and apply triangle law of vector, we get

Substitute the values from eqn(ii) an eqn(iii) in eqn(i), we get

Therefore, AB is parallel to DC and equal is magnitude.

Hence, ABCD is a parallelogram.

Hence proved