1. A three-dimensional (3D) space touch apparatus, comprising: an infrared Light-Emitting Diode (LED) array; left and right infrared cameras; a support that supports the infrared LED array and the left and right infrared cameras, wherein the infrared LED array emits infrared rays to form an infrared screen having a predetermined shape in a space above the support, and wherein the left and right infrared cameras are disposed on left and right sides of the support so that lenses thereof can be oriented to the infrared screen; and a space touch sensor module that calculates X-axis, Y-axis and Z-axis coordinates of a selected location in the infrared screen, touched by user pointing means, using scattering or diffusion of the infrared rays generated in images including the selected location captured by the left and right infrared cameras when the selected location is touched by the user pointing means, wherein the space touch sensor module: calculates the Z-axis coordinate of the selected location in the infrared screen by dividing a vertical-axis coordinate of locations, corresponding to the selected location of the camera images touched by the user pointing means, by a resolution of the left and right infrared cameras, and multiplying a result of the division by a predetermined distance of the Z-axis; and calculates the X-axis and Y-axis coordinates of the selected location in the infrared screen using lateral-axis coordinates of the locations in the camera images touched by the user pointing means and information about angles of view of the left and right infrared cameras.