Differential reaction cross sections for the K + CH3Br --> KBr + CH3 reaction are obtained in a crossed beam experiment with brute force oriented and nonoriented CH3Br molecules at a collision energy of 1.3 eV. Analysis of the angular distribution and the time-of-flight spectra of reactions with nonoriented CH3Br molecules leads to the conclusion that the KBr products are preferentially sideward scattered with a most probable recoil velocity of 70% of the maximum value. The angle-dependent steric asymmetry, or steric effect, is obtained by orienting the CH3Br molecules and measuring the difference in KBr product flux for collisions of K with the Br end and CH3 end of CH3Br, respectively. The angular distribution of the steric asymmetry indicates that KBr products are most likely formed for collision geometries deviating 40 degrees from a pure collinear CH3Br-K collision geometry. Results of this study are compared with those of the analogous reaction, K + CH3I --> KI + CH3. The average translational energy of the products is found to be only slightly larger than that obtained for thermal collision energies.