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ABCD is a parallelogram whose diagonals ...

`ABCD` is a parallelogram whose diagonals meet at P. If O is a fixed point, then `vec(OA)+vec(OB)+vec(OC)+vec(OD)` equals :

A

(a) `vec(OP)`

B

(b) `2vec(OP)`

C

(c) `3vec(OP)`

D

(d) `4vec(OP)`

Text Solution

Verified by Experts

The correct Answer is:
D
We know that, P will be the mid-point of AC and BD.

`thereforeOA+OC=2OP` . . . (i)
and `OB+OD=2OP`
On adding Eqs. (i) and (ii), we get
`OA+OB+OC+OD=4OP`
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