Let `A B C D`be a p[arallelogram whose diagonalsintersect 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`

Let `A B C D`be a p[arallelogram whose diagonalsintersect at `P`and le

1.	Let `A B C D`be a p[arallelogram whose diagonalsintersect 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`
Answer» Since the diagonals of a parallelogram bisect each other, P is the middle point of AC and BD both. Therefore, `vec(OA) + vec(OC) = 2 vec(OP) and vec(OB) + vec(OD) = 2 vec(OP)`

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Let `A B C D`be a p[arallelogram whose diagonalsintersect 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`

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