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The volume of the tetrahedron ABCD with vertices A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3) and D(x4, y4, z4) is

V = (1/6)|((x1,y1,z1,1),(x2,y2,z2,1),(x3,y3,z3,1),(x4,y4,z4,1))|

The volume of tetrahedron formed by the planes x + y = 0, y + z = 0, z + x = 0 and x + y + z = 1 is

(a) 2/3 

(b) 4/3

(c) 8/3 

(d) 10/3

1 Answer

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Answer is (a) 2/3

On solving, we get the vertices of a tetrahedron as (0, 0, 0, 0), (1, 1, –1), (1, –1, 1), (–1, 1, 1).

Volume of a tetrahedron

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