The drag force on a sphere in tangential and normal motion to a plane wall is evaluated in the limit of large Knudsen number and small Mach (and Strouhal) number assuming isothermal conditions and diffuse reflection of gas molecules on walls. In the limit of free molecular flow, the molecular distribution function of the gas is evaluated using a set of coupled Fredholm integral equations. The results are compared with direct simulation Monte Carlo calculations and extended for finite Knudsen numbers. In all cases stronger dependence of the force on the width of the gap is found for normal compared to tangential motion. When the flow within the gap can be considered as essentially collisionless in nature, a similar dependence of the force on the gap width is observed at finite Knudsen numbers as in the free molecular case.