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If three concurrent edges of a parallelopiped of volume `V` represent vectors `veca,vecb,vecc` then the volume of the parallelopiped whose three concurrent edges are the three concurrent diagonals of the three faces of the given parallelopiped is

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The three concurrent edges of a parallelopiped represents the vectors bar(a),bar(b),bar(c) such that [bar(a)bar(b)bar(c)]=lambda. Then the volume of the parallelopiped whose three concurrent edges are the threeconcurrent diagonals of three faces of the given parallelopiped is-

If the volume of a parallelopiped whose three coterminal edges are represented by vectors, then lambda =________.

Knowledge Check

  • The three concurrent edges of a parallelopiped represent the vectors veca, vecb, vecc such that [(veca, vecb, vecc)]=V . Then the volume of the parallelopiped whose three concurrent edges are the three diagonals of three faces of the given parallelopiped is

    A
    `2V`
    B
    `3V`
    C
    `V`
    D
    `6V`

  • Statement 1: Let veca, vecb, vecc be three coterminous edges of a parallelopiped of volume V . Let V_(1) be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then V_(1)=2V . Statement 2: For any three vectors, vecp, vecq, vecr [(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]

    A
    1
    B
    2
    C
    3
    D
    4

  • The volume of a parallelopiped whose coterminous edges are 2a, 2b, 2c, is

    A
    `2 [(a,b,c)]`
    B
    `4 [(a,b,c)]`
    C
    `8 [(a, b, c)]`
    D
    `[(a,b,c)]`

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    The volume of the parallelopiped constructed on the diagonals of the faces of the given rectangular parallelopiped is m times the volume of the given parallelopiped. Then m is equal to

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