1. A spatial motion recognition system, comprising: a motion detection unit for outputting position changes of a body of the system in space as an electric signal based on three-dimensional motions of the system body; a control unit for receiving the electric signal outputted from the motion detection unit, wherein the control unit: tracks the three-dimensional motions of the system body based on the electric signal outputted from the motion detection unit, produces a virtual handwriting plane located in three-dimensional space, wherein a location of the virtual handwriting plane is a plane which is most adjacent to a set of respective points which correspond to the tracked three-dimensional motions of the system body in predetermined time intervals, and projects the respective points corresponding to the tracked three-dimensional motions of the system body in the predetermined time intervals onto the virtual handwriting plane as motion tracks, carries out a rotation conversion of the motion tracks projected on the virtual handwriting plane into a two-dimensional plane of x and y axes; and a display unit for displaying the two-dimensional plane outputted by the control unit.