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Volume of tetrahedron formed by the plan...

Volume of tetrahedron formed by the planes `x+y=0, y+z=0, z+x=0,x+y+z-1=0` is

A

`(1)/(6)`

B

`(1)/(3)`

C

`(2)/(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Solving the planes taking 3 at a time
Vertices of tetrahedron are
`O: (0,0,0), A: (1,1,-1),B:(1,-1,1),C:(-1,1,1)`
`implies "Volume"=(1)/(3) xx("area of base")xx("height")`
`=(1)/(3)xxsqrt(3)/(4)xx(2sqrt(2))^(2)xx(1)/sqrt(3)=(2)/(3)`
Or Volume `=(1)/(6)[vec(a) vec(b) vec(c)]`
`("where" vec(a)=vec(OA), vec(b)=vec(OB) and vec(c) = vec(OC))`
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Knowledge Check

  • The direction of the line of intersection of the planes 2x + 3y + z-1 = 0 and x+y-z-7 = 0 is ..............

    A
    (-4,-3,1)
    B
    (-4,3,1)
    C
    (4,3,1)
    D
    (4,-3,1)

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