Question

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

• A. V £$\frac { 9 } { 2 }$
• B. V ³$\frac { 9 } { 2 }$
• C. V = $\frac { 9 } { 2 }$
• D. None of these

Answer 1

Answer: (B)

V ³$\frac { 9 } { 2 }$

Answer 2

Let the equation of the plane be + + = 1

Ž $\frac { 1 } { \mathrm { a } }$ + $\frac { 1 } { \mathrm {~b} }$ += 1

Ž Volume of tetrahedron OABC = V = $\frac { 1 } { 6 }$ (abc)

Now (abc)^1/3 ³ ³ 3

Ž abc ³ 27

Ž V ³