Dear Student
Force of gravity always act towards the centre of the earth , so when an object is thrown up,the force of gravity will act in opposite direction of motion,that's towards the centre of earth.
Acceleration due to gravity is the acceleration gained by an object due to the force of gravity. It is vector quantity having magnitude of 9.806m/s2 and direction as well.
So for a free falling object acceleration due to gravity is directed downward as acceleration of a body always takes the direction of the net force acting on that body, and since the only force we are considering is that of gravity, then this acceleration should take the direction of gravity, i.e., downward.
Hence acceleration due to gravity is vector quantity as it has magnitude as well as direction.
Regards