Q3 of 177 Page 23

ABCD is a parallelogram and P is the point of intersection of its diagonals. If O is the origin of reference, show that

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.


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