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; and a control unit for tracking three-dimensional motions of the system body based on the electric signal outputted from the motion detection unit, producing a virtual handwriting plane having the shortest distances with respect to respective positions in predetermined time intervals based on three-dimensional track information obtained through tracking, and projecting the respective positions in the predetermined time intervals onto the virtual handwriting plane to recover the motions in space.