Problem

Relative to a fixed origin O, the points A, B, C and D have coordinates $(0, 4, 1)$, $(4, 0, 0)$, $(3, 5, 2)$ and $(2, 2, k)$ respectively, where $k$ is a constant.

(a) Determine the exact area of triangle ABC.

(b) Determine in terms of $k$, the volume of the tetrahedron ABCD, simplifying your answer.