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