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__Exercise__: Prove that if a body moves under the action of a force F = k⋅u × v, where u is an arbitrary unit vector and v the velocity, the motion is circular with angular velocity ω = k ⋅ u or, in a more general case, a spiral parallel to u.

Source: (Alonso & Finn: Fundamental university physics)

I attempted to prove that F is a central force, so that the angular momentum is constant. Is that wrong?

Thank you in advance!