If `G` is the intersection of diagonals of a parallelogram `A B C D` and `O` is any point then `O vec A+O vec B+O vec C+O vec D=`
a.`2 vec OG`
b. `4 vec OG`
c. `5 vec OG`
d. `3 vec OG`

Options

A. ` 2 vec(OG)`
B. `4 vec(OG)`
C. `5 vec (OG)`
D. `3 vec (OG)`

Answer

B

Explanation

Talking O as the origin, let the position vectors of A, B, C and D be ` vec a , vec b , vec c and vec d ` respectively.
In `Delta` OAC, G is the mid-point of AC.
` O vec A + O vec C = 2 O vec G " " ` (i)
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In `Delta OBD,` G is the mid-point of BC.
` therefore O vec B + O vec D = 2 O vec G " " ` (ii)
Adding (i) and (ii) , we get
`O vec A + O vec B + O vec C + O vec D = 4 O vec G `