Successful imaging is demonstrated of the three individual Cartesian components of the vector magnetic field from a magnetized surface. This is accomplished by exploiting the capability of the magnetic force scanning tunneling microscope to generate two-dimensional mapping of definite combinations of orthogonal magnetic-field components. This method is applied to well-characterized patterns on thin-film longitudinal recording media and some peculiar characteristics of recorded magnetization patterns are found, including the presence of a significant cross-track magnetization component persisting along the track edges. The experimental approach and the unique physical insights acquired by simultaneously investigating individual magnetic-field components are discussed.