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Find the volume of tetrahedron formed by...

Find the volume of tetrahedron formed by the four planes `barr. (bari + barj) = 0 , barr. (barj + bark) = 0, barr. (bari + bark) = 0` and `barr. (bari + barj + bark) = 4.`

Text Solution

Verified by Experts

The correct Answer is:
`128/3`
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Explore conceptually related problems

Find the volume of the tetrahedron formed by the points 3bari+4barj,bari+barj,3bari-barj,3barj+2bark .

Find the volume of the tetrahedron having the coterminus edges 2bari + barj +bark, bari -3barj +2bark, bari -bark .

Knowledge Check

  • (bari-barj) xx (barj-bark).(bark-bari) =

    A
    0
    B
    1
    C
    2
    D
    3

  • The angle between the line of intersection of the two planes barr. (2bari+2barj-3bark)=5, barr.(3bari+3barj-5bark)=3 and the line barr=3bari + 2barj + bark + t (5bari + 5barj- 7bark) is

    A
    `cos^(-1)((-1)/sqrt28)`
    B
    `cos^(-1)(41/(sqrt(17)sqrt(99)))`
    C
    `pi/2`
    D
    `pi/3`

  • The angle between the planes barr.(2bari+barj+bark)=5, (bari-barj+2bark)=3 is

    A
    `30^(@)`
    B
    `45^(@)`
    C
    `60^(@)`
    D
    `90^(@)`

    • Similar Questions

    Explore conceptually related problems

    If bara = bari - 2barj - 3bark , barb= 2bari + barj - bark , barc = bari + 3barj - 2bark find bara xx (barb xx barc) .

    Find the value of lamda for which the four points with position vectors bari - 2barj + bark, 2bari - barj + lamdabark , 2bari + barj -bark and 3bari + barj - bark are coplanar.

    Find the distance of a point (2, 5, -3) from the plane, barr.(6bari-3barj+2bark) = 4

    Prove that the four points 4bari + 5barj +bark, - (barj + bark) , 3bari + 9barj + 4bark , - 4bari + 4barj +4bark are coplanar.

    The acute angle between = barr. (-bari+3bark)+lambda (2bari+3barj+ 6bark) and barr (10bari + 2barj - 11bark)=3 is ,

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