We describe a conceptually and experimentally simple approach for quantum-state-resolved measurement of the full three-dimensional recoil velocity distribution of the products from photodissociation or photoinitiated chemical reaction. The method uses pulsed lasers to determine two components of the recoil velocity vector, by spatial displacement of a probe laser beam relative to a photolysis laser beam, so we call this method POSTS, for position sensitive translational spectroscopy. The third component of the velocity vector is obtained from Doppler selection, ion time-of-flight mass spectrometry, spatial masking of a detector, or use of a one-dimensional array detector. POSTS requires only a single probe laser, and it is not essential that this laser have a narrow frequency bandwidth. Its TOF measurements can be made with very high resolution on a spatial scale as small as 0.1 cm. POSTS will work with all atomic and molecular species having any magnitude of recoil velocity, and with most pulsed-laser detection techniques. We demonstrate the capabilities of the POSTS method by velocity measurements on the H atoms from photodissociation of HI, and HCL molecules from the vibrational predissociation of (HCl)(2). In the latter case the high resolution capabilities of POSTS allow a determination of the bond dissociation energy of the HCl dimer to an accuracy of +/-1 cm(-1) from. TOF measurements on a spatial scale of only 0.1 cm.