That's because technically N.m is the magnitude of either of the energy and torque bivectors; technically the product you should use is the scalar product for t

That's because technically N.m is the magnitude of either of the energy and torque bivectors; technically the product you should use is the scalar product for the energy, and the wedge product for the torque. You could use the geometric product too and just call both [(N.v1)(m.v2)] for vectors v1 and v2; you would even get as a result [(N.v1)(m.v2)] = [N.v1*m.v2 + N.v1^m.v2] = [(N.v1*m.v2)] + [(N.v1)^(m.v2)] = [Energy part] + [Torque part], which is kind of neat - units that depend on the angles involved but encompassing both cases