In this paper, the relationships of the plunges and azimuths of T and P axes versus the strikes, dips, and rakes of two seismic nodal planes were derived to provide reference for earthquake researchers. The independence of the plunges and azimuths of T, B, and P axes in focal mechanism solution was discussed, and it was concluded that three parameters, i.e., the azimuths of T, B and P axes, are completely independent. The focal mechanism solution representation based on Euler rotation was introduced,using three Euler angles in place of the plunges and azimuths of T, B, and P axes, and three focal mechanism solution representations were briefly compared and analyzed in respect of accuracy on the basis of the assumption of rounding; it was concluded that the Euler angle representation has better accuracy, compared with the azimuth representation and the traditional representation with T, B,and P axes. In this paper, the relationships of the plunges and azimuths of T and P axes versus the strikes, dips, and rakes of two seismic nodal planes were derived to provide reference for earthquake researchers. The independence of the plunges and azimuths of T, B, and P axes in focal mechanism solution was discussed, and it was done that three parameters, ie, the azimuths of T, B and P axes, are completely independent. The focal mechanism solution representation based on Euler rotation was introduced, using three Euler angles in place of the plunges and azimuths of T, B, and P axes, and three focal mechanism solution representations were briefly compared and analyzed in respect of accuracy on the basis of the assumption of rounding; it was concluded that the Euler angle representation has better accuracy, compared with the azimuth representation and the traditional representation with T, B, and P axes.