Question #41269

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-coplanar vectors such that their scalar triple product $[\vec{a} \ \vec{b} \ \vec{c}] = V$. Consider the determinant $\Delta = \begin{vmatrix} (\vec{a}\times\vec{b})\cdot(\vec{c}\times\vec{a}) & (\vec{a}\times\vec{b})\cdot(\vec{b}\times\vec{c}) & |\vec{a}\times\vec{b}|^2 \\ (\vec{b}\times\vec{c})\cdot(\vec{c}\times\vec{a}) & |\vec{b}\times\vec{c}|^2 & (\vec{b}\times\vec{c})\cdot(\vec{a}\times\vec{b}) \\ |\vec{c}\times\vec{a}|^2 & (\vec{c}\times\vec{a})\cdot(\vec{b}\times\vec{c}) & (\vec{c}\times\vec{a})\cdot(\vec{a}\times\vec{b}) \end{vmatrix}$ Which of the following represents the value of $\Delta$?