Problem 15ΒΆ

Compute the mixed volume of the following three triangles in \(\mathbb{R}^3\):

\[\begin{split}\begin{matrix} T_1 = {\rm conv}((2a,2a,2a),(0,a,a),(1,0,0)), \\ T_2 = {\rm conv}((2a,2a,2a),(a,0,a),(0,1,0)), \\ T_3 = {\rm conv}((2a,2a,2a),(a,a,0),(0,0,1)). \end{matrix} \qquad \quad {\rm for}\,\,a \in \mathbb{N}.\end{split}\]