Final answer:
The direction of the magnetic field B⃗ a at point A is North to South.
Step-by-step explanation:
The direction of the magnetic field B⃗ a at point A depends on the orientation of the bar magnet. If the north pole of the compass needle points towards point A, then the direction of the magnetic field at point A is the same as the direction in which the north pole of the compass needle points.
Since the north pole of the compass needle points towards the north pole of the bar magnet, the direction of the magnetic field B⃗ a at point A is North to South.