Heater control valves are operated by which of the following mechanisms?

Heater control valves are responsible for regulating the flow of coolant or hot water to the heater core in a vehicle's heating system. They typically utilize a combination of mechanisms to operate effectively, which is why the option indicating a combination of cable, thermostat, and vacuum motor is the correct answer.

The use of a cable allows for manual adjustments from the driver's seat, while the thermostat helps monitor the temperature and signals when the heater valve should open or close based on the cabin temperature. Additionally, vacuum motors are commonly employed in older vehicle systems, utilizing vacuum pressure generated by the engine to actuate the valve. This multi-faceted approach provides precise control over the heating system, ensuring that it can respond effectively to changing temperature needs within the cabin.

Other options like the electric motor and pneumatic control, while applicable in certain systems, do not encompass the traditional and widely used mechanisms found in many vehicle heating systems. The comprehensive nature of the correct answer reflects how varied technologies work together to achieve optimal heating control.