A plane passing through `(1,1,1)` cuts positive direction of coordinates axes at `A ,Ba n dC ,` then the volume of tetrahedron `O A B C` satisfies a. `Vlt=9/2` b. `Vgeq9/2` c. `V=9/2` d. none of these

Options

A. `Vle(9)/(2)`
B. `Vge(9)/(2)`
C. `V=(9)/(2)`
D. none of these

Answer

b

Explanation

Let the equation of the plane be `(x)/(a)+(y)/(b)+(z)/(c)=1`
`implies(1)/(a)+(1)/(b)+(1)/(c)=1`
`implies` Volume of tetrahedron OABC `=V=(1)/(6)(abc)`
Now `(abc)^(1//3)ge(3)/((1)/(a)+(1)/(b)+(1)/(c))ge3(G.M.geH.M)`
or `abcge27impliesVge(9)/(2)`