Let T be a tetrahedron in standard position, with three edges along the three positive coordinate axes in R 3 , and suppose the vertices are ae 1 , be 2 , ce 3 , and 0, where e 1 e 2 e 3 I 3 Find formulas for the barycentric coordinates of an arbitrary point p in R 3 ...

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Let T be a tetrahedron in standard position, with three edges along the three positive coordinate axes

Question:

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 [e₁ e₂ e₃] = I₃. Find formulas for the barycentric coordinates of an arbitrary point p in R³.