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

Let the equation of the plane in intercept form be xa+yb+zc=1…………. (1)  Where a,b,c are positive intercepts on coordinate axes.  Eq. (1)_ ) is passing through (1,1,1)⇒1a+1b+1c=1 We know that Volume of the tetrahedron OABC=V=16(abc) Using the inequality Geometric mean (G.M.) ≥ Harmonic mean (H.M.) ⇒(abc)13≥31a+1b+1c⇒(abc)13≥31⇒abc≥27⇒16(abc)≥16(27)⇒V≥92Therefore, the correct answer is (2).