Let be the position vectors of the four distinct points A, B, C, D. If then show that ABCD is a parallelogram.

Given the position vectors of points A, B, C and D are,, and respectively.

Recall the vector is given by

Similarly, the vector is given by

But, it is given that.

Two vectors are equal only when both their magnitudes and directions are equal.

and.

This means that the opposite sides in quadrilateral ABCD are parallel and equal.

Thus, ABCD is a parallelogram.