A position determining system is disclosed, which has a simplified configuration capable of producing a plurality of phantom planes simultaneously. The improved system according to the present invention consists of a light receiving and sensing device that includes a body having means for sending data on elevation- and depression-angles and horizontal angles, and a phantom plane determining function for determining phantom planes, so as to display or output differential angles of elevations and depressions in relation with the phantom surfaces produced from the data received from the body.