Magnetic field is a

Concept — A physical quantity is classified by what must be supplied to specify it completely. A scalar needs only a magnitude with its unit. A vector needs a magnitude together with a direction in space, and two vectors of the same kind combine by the triangle or parallelogram law instead of ordinary arithmetic addition. "Dimensionless" is a separate label on a different axis: it marks a quantity whose dimensional formula reduces to M0 L0 T0, so its measure is a pure number that does not depend on any choice of unit such as the metre or the tesla.

Application — Apply the test to the magnetic field at a point:

• It is defined through the magnetic force law F = q(v × B). The force on a moving charge depends on how the field is oriented relative to the velocity, so a bare number cannot specify the field — an orientation must be supplied with it.

• That direction is physically observable: a freely pivoted magnetic needle placed at the point settles along it, while an ordinary compass, being constrained to the horizontal plane, settles along the horizontal component of the field. The field is drawn as the tangent to the magnetic field line through that point.

• Two magnetic fields acting at the same point add by the parallelogram law, not arithmetically: 3 T and 4 T at right angles give a resultant of 5 T, not 7 T.

Specifying the magnetic field therefore requires a magnitude and a direction, which is exactly the definition of a vector quantity.

Cross-check — test each label against what the magnetic field at a point actually offers.

Fine print worth knowing: the magnetic field is an axial (pseudo) vector — it behaves differently from an ordinary vector under mirror reflection. It still carries magnitude and direction and still obeys vector addition, so under the scalar / vector / dimensionless classification used here it sits with the vectors.

Result — the magnetic field is a vector quantity.