Suppose \(\vec{u}\), \(\vec{v}\) and \(\vec{w}\) are vectors in 3D, where \(\vec{u} = (u_1, u_2, u_3)\); \(\vec{v} = (v_1, v_2, v_3)\) and \(\vec{w} = (w_1, w_2, w_3)\).
Express \((\vec{u} \times \vec{v}) \cdot \vec{w}\) as a determinant.
Compute and find a relation between the expressions