Why is a magnetic field a vector quantity?

This direction is independent of the test dipole, and only depends on the orientation and distance of the magnetic dipole. The force this unit dipole experiences, is the magnetic field at that point. As you can see, this quantity requires a unique direction for compete understanding. Therefore, it is a vector quantity.

Explanation:

This direction is independent of the test dipole, and only depends on the orientation and distance of the magnetic dipole. The force this unit dipole experiences, is the magnetic field at that point. As you can see, this quantity requires a unique direction for compete understanding. Therefore, it is a vector quantity.