A) \[V\le \frac{9}{2}\]
B) \[V\ge \frac{9}{2}\]
C) \[V=\frac{9}{2}\]
D) None of these
Correct Answer: B
Solution :
[b] Let the equation of the plane be \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\] \[\Rightarrow \frac{1}{a}+\frac{1}{b}+\frac{1}{c}=1\] \[\Rightarrow \] Volume of tetrahedron \[OABC=V=\frac{1}{6}(abc)\] Now, \[{{(abc)}^{1/3}}\ge \frac{3}{\frac{1}{a}+\frac{1}{b}+\frac{1}{c}}\ge 3(GM.\ge H.M.)\] or \[abc\ge 27\Rightarrow V\ge \frac{9}{2}\]
You need to login to perform this action.
You will be redirected in
3 sec
