Figure 19 depicts a tetrahedron whose faces lie in the coordinate planes and in the plane with equation The volume of the tetrahedron is given by V 1 6 abc Find the minimum value of V among all planes passing through the point P (1, 1, 1) X a y b Z 1 (a,b,c 0) ...

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Figure 19 depicts a tetrahedron whose faces lie in the coordinate planes and in the plane with

Question:

Figure 19 depicts a tetrahedron whose faces lie in the coordinate planes and in the plane with equation X a + y b + Z = 1 (a,b,c > 0). The volume of the tetrahedron is given by V = 1/6 abc. Find the minimum value of V among all planes passing through the point P = (1, 1, 1).