Question

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

Answer 1

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