A plane passing through (1, 1, 1) cuts positive direction of coordinate axes at A, B and C, then the volume of tetrahedron OABC satisfies

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V≤92

V≥92

V=92

none of these

answer is B.

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Detailed Solution

Let the equation of the plane be xa+yb+zc=1⇒ 1a+1b+1c=1⇒ Volume of tetrahedron OABC=V=16(abc) Now (abc)1/3≥31a+1b+1c≥3 (G.M. ≥ H.M.)or abc≥27⇒V≥92

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