What should be the first action in case of an engine fire in flight?

In the event of an engine fire in flight, cutting off the mixture to the engine is indeed a critical first action. This is because the mixture controls the fuel-to-air ratio entering the engine. By moving the mixture control to the "idle cut-off" position, you effectively stop the flow of fuel to the engine, which can help to extinguish the fire by eliminating its fuel source.

It is essential to address the fuel flow promptly, as allowing fuel to continue to flow into a burning engine can exacerbate the situation and make it more difficult to manage the fire safely. Additionally, addressing the fuel supply first helps to mitigate the risks associated with both the fire and the impending loss of engine power.

Establishing a glide, shutting off electrical systems, or opening the fuel selector may be necessary follow-up actions, but they do not directly solve the immediate problem of managing an engine fire. The most effective first step is always to eliminate potential fuel sources feeding the fire in order to enhance safety and regain control of the aircraft.