# the force being perpendicular to both the velocity and the field as result of the tensor's anti-symm

The anti-symmetric nature of the magnetic field's tensor representation is the fundamental mathematical reason why the resulting force on a charged particle is always perpendicular to both the field and the particle's velocity. It shows how the zero diagonal elements and the opposite-signed off-diagonal pairs in the tensor directly correspond to the rotational effect of the Lorentz force.

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