When one refers to the strength of a magnetic field, they're usually referring to the scalar magnitude of the magnetic field vector, so no.
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Vector.
A magnetic field is neither: it is a vector field with both direction and quantity.
Charge is not a vector.
for a vector quantity it must have both magnitude and direction and since it has both magnitude and direction it is therefore considered a vector
Magnetism is a force. Vector notation is required to indicate magnitude and direction of a force.