If vector a, vector b, vector c and vector d are the position vectors of points A, B, C, D such that no three of them are collinear

Question

If  \(\vec a,\,\vec b, \,\vec c \) and \(\vec d\) are the position vectors of points A, B, C, D such that no three of them are collinear and \(\vec a+\vec b+\vec c\) = \(\vec b+\vec d,\) then ABCD is a

A. rhombus

B. rectangle

C. square

D. parallelogram

Answer 1

Correct option is D. parallelogram

Multiplying the above mentioned equation by \(\cfrac12\),

So, the position vector of mid – point of BD = Position Vector of mid - point of AC.

Hence the diagonals bisect each other.

Therefore the given figure ABCD is a parallelogram.