A new method for determining the forces between colloidal particles is presented, based on observing the changes in two-particle collision trajectories in a linear shear flow and inverting the trajectory equations describing such collisions. In the absence of colloidal forces and under low Reynolds number conditions, collisions are symmetric and reversible. When colloidal forces are acting between the particles, this symmetry is broken, and the degree of asymmetry is a measure of the magnitude of colloidal forces. From a sufficiently large number of experimentally observed collision trajectories we can determine the colloidal forces by a minimization method, assuming some relationship between the interaction force and interparticle distance. This relationship can either be taken from theory, e.g., classical DLVO theory, or be represented by a general function of interparticle distance with adjustable parameters which can be determined from the best fit between theory and experiment. From Monte Carlo simulations it has been found that the number of collisions required for a reliable determination of the colloidal force-distance relationship is about 25. Some experiments have been done with a "surface collision apparatus", which we describe in detail. The results for latex particles in mixtures of glycerol-water and D2O-water show that the method is capable of detecting forces that are 3-4 orders of magnitude smaller than those measured by a conventional surface force apparatus or by atomic force microscopy. A minimization analysis of data obtained previously with the traveling microtube apparatus is also presented.