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Let A B C D be a p[arallelogram whose di...

Let `A B C D` be a p[arallelogram whose diagonals intersect at `P` and let `O` be the origin. Then prove that ` vec O A+ vec O B+ vec O C+ vec O D=4 vec O Pdot`

A

`OP`

B

`2 OP`

C

`3 OP`

D

`4 OP`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, the diagonals of a paralelogram bisect each other. Therefore, P is the middle point of AC and BD both.
`:." "OA + OC = 2 OP" and "OB+OD=2OP`
`rArr" "OA+OB+OC+OD=4 OP`
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