As the plane π parallel to b = (1, 0, –1) and c = (– 1, 1, 0) normal to the plane is given by
∴ The equation of the plane ABC is
1.(x – 1) + 1.(y – 1) + 1.(z – 1) = 0
x + y + z – 3 = 0
x + y + z = 3
x/3 + y/3 + z/3 = 1.
This planes meets the axes in A(3, 0, 0), B(0, 3, 0), C(0, 0, 3).
Thus, volume of the tetrahedron OABC