ABCD is a parallelogram and P is the point of intersection of its diagonals,if O is the origin of reference, show that OA vector+OB vector+O

Question

ABCD is a parallelogram and P is the point of intersection of its diagonals,if O is the origin of reference, show that OA vector+OB vector+OC vector+OD vector=4OP vector​

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Serenity 4 weeks 2021-11-02T06:37:24+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-02T06:38:49+00:00

    Step-by-step explanation:

    ANSWER

    OA

    +

    OB

    +

    OC

    +

    OD

    =(

    OP

    +

    PA

    )+(

    OP

    +

    PB

    )+(

    OP

    +

    PC

    )+(

    OP

    +

    PD

    )

    =4

    OP

    +(

    PA

    +

    PD

    +

    PB

    +

    PC

    )

    =4

    OP

    +(

    PA

    PA

    +

    PB

    PB

    )

    ( ∵ For a parallelogram P bisects the two diagonal.)

    =4

    OP

    Hence, A is the correct option.

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