`A B C D` is parallelogram and `P` is the point of intersection of its diagonals. If `O` is the origin of reference, show that ` vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot`

Options

A. `4vec(OP)`
B. `2vec(OP)`
C. `vec(OP)`
D. Null vector

Answer

A

Explanation

`:' vec(OA)=vec(OP)-vec(AP),vec(OB)=vec(OP)+vec(PB),`
`vec(OC)=vec(OP)+vec(PC)& vec(OD)=vec(OP)-vec(DP)`,
Also, `vec(AP)=vec(PC)& vec(DP)=vec(PB)`
`:.vec(OA)+vec(OB)+vec(OC)+vec(OD)=4vec(OP)`