Airplane engines require air to work, that is conspicuously lacking in space. A rocket plane could go to space.

Engines propel by moving molecules from the front of the craft to the back of the craft, hence using a turbofan (move air from front to back with a fan powered by a turbine) or a rocket (blow a mixture of hydrogen and oxygen from the front of the craft out the rear) - a rocket can work in space because I am not relying on atmospheric mass (the air molecules) for propulsion. In space, gas molecules are too far apart for this to work.

The term for this is 'reaction mass' or 'where do I get stuff to toss behind me to make me go forward?'