"The plane cannot take off."
不可以 Actually means "not allowed". If it was supposed to mean "can't" then should be 不能
It depends on why the plane couldnt take off. If something was wrong with it and it could not fly, use 不能，but if say permission by air traffic control was not granted for the plane to take off, then its not allowed so use 不可以. But this sentence gave no context.