The correct answer is B) provide close vane to rotor and blade to stator case clearances. The metal spray rub coating on the rotor and stator casing of an axial type compressor is used to maintain tight clearances between the rotating and stationary components. This helps to optimize the compressor's aerodynamic efficiency by minimizing air leakage between the rotor blades and stator vanes. The close clearances allow the compressor to operate at peak performance. The other answer choices are incorrect because they do not accurately describe the primary purpose of the metal spray rub coating. Option A is incorrect as the coating does not directly control airflow. Option C is incorrect as the coating is not used to seal dovetail joints. Option D is incorrect as the coating is not for protecting the gearbox adapter.