\left( a_{1} ,a_{2} ,a_{3} \right) \ast \left( \left( b_{1} ,b_{2} ,b_{3} \right) \ast \left( c_{1} ,c_{2} ,c_{3} \right) \right) = \left( a_{2} b_{1} c_{2} - a_{2} b_{2} c_{1} - a_{3} b_{3} c_{1} + a_{3} b_{1} c_{3} ,