Er.. I'm not Einstein ;-) but I'll try and put you on the right track... The term "magnetic vector" refers to the amplitude and direction of the magnetic field associated with an electromagnetic wave. Hope this helps!
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If you apply a magnetic field to matter (i.e. a piece of iron) then preexisting magnets on the atomic level align with the magnetic field. The strength on direct of this orientation is described by the magnetization vector.
Vector.
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.
Magnetic moment is a vecotr quantity
Charge is not a vector.
Magnetism is a force. Vector notation is required to indicate magnitude and direction of a force.