Q32 of 177 Page 23

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.


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