If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then vector(OA) + vector(OB) + vector(OC) + vector(OD) =

Question

If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then  \(\vec{OA}+\vec{OB}+\vec{OC}+\vec{OD}=\)

A. \(2\,\vec{OG}\)

B.  \(4\,\vec{OG}\)

C. \(5\,\vec{OG}\)

D. \(3\,\vec{OG}\)

Answer 1

 Correct option is B. \(4\,\vec{OG}\)
 

Let us consider the point O as origin.

G is the mid – point of AC.

Also, G is the mid− point of BD,