Chapter 8.2, Problem 18E

Let T be a tetrahedron in “standard” position, with three edges along the three positive coordinate axes in ℝ³, and suppose the vertices are ae₁, be₂, ce₃, and 0, where $\left[\begin{array}{ccc}{\text{e}}_{\text{1}}& {\text{e}}_{\text{2}}& {\text{e}}_{\text{3}}\end{array}\right]=I_3$. Find formulas for the barycentric coordinates of an arbitrary point p in ℝ³.