A system for positioning a tool relative to a workpiece includes a movable table for accommodating a workpiece, and executing movements in two main moving directions during processing of the workpiece, one or more planar measuring standards provided in stationary fashion about the tool and extend in the plane of the main moving directions, and scanning heads, mounted in at least three corners of the table, for detecting the position of the table relative to the measuring standards. The position of the table is determinable by the scanning heads in six degrees of freedom. In at least one of the corners, one or more scanning heads having a total of at least three measuring axes is/are provided for 3-D position detection in three independent spatial directions. Sensitivity vectors of the measuring axes for the 3-D position detection are neither parallel to the X-Z plane nor parallel to the Y-Z plane.