[QUE/ME-02015] ME-PROBLEM

Show that \begin{equation*} [\vec{A},\vec{B},\vec{C}]^2 = \begin{vmatrix} \vec{A}.\vec{A} & \vec{A}.\vec{B} & \vec{A}.\vec{C} \\ \vec{B}.\vec{A} & \vec{B}.\vec{B} & \vec{B}.\vec{C} \\ \vec{C}.\vec{A} & \vec{C}.\vec{B} & \vec{C}.\vec{C} \end{vmatrix} \end{equation*} where \([\vec{A},\vec{B},\vec{C}]=\vec{A} . (\vec{B} \times \vec{C} ). \)