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Show that the sum of the vectors represe...

Show that the sum of the vectors represented by the sides `bar(AB),bar(DC)` of a quadrilateral ABCD as equivalent to the sum of the vectors represented by the diagonals `bar(AC) and bar(DB)`.

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Knowledge Check

  • The three vectors bar(OA), bar(OB) and bar(OC) have the same magnitude R. Then the sum of these vectors have magnitude.

    A
    R
    B
    `sqrt(2)R`
    C
    3R
    D
    `(1 + sqrt(2))R`

  • If D is the mid -point of side AB of DeltaABC , then bar(AB) + bar(BC) + bar(AC) =

    A
    `2(bar(AD)-bar(BD))`
    B
    `2(bar(DC)-bar(BD))`
    C
    `2(bar(BD)-bar(CA))`
    D
    `2(bar(BD)-bar(AC))`

  • If ABCD is quadrilateral whose sides represent vectors in cyclic order, vecAB is equivalent is

    A
    `vec(CA)+vec(CB)`
    B
    `vec(CD)`
    C
    `vec(AD)+vec(DC)+vec(CB)`
    D
    `vec(AD)+vec(BD)`

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    The vector area of a parallelogram with bar(a) and bar(b) as adjacent sides is

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