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Power is the time derivative of energy, E. Energy can be scalar or vector. Thus power can be scalar or vector. Energy is a quaternion and consists of a scalar or real part Er and a vector part Ev. Energy E=Er + Ev, for example E= FR = -F.R + FxR = -FRCos(x) + FRsin(x). The real part is a scalar called "Energy" and the vector part is called "Torque" but has the same units Joules. Energy is defined by the units.

P=dE/dt = d(Er + Ev)/dt = dEr/dt + dEv/dt = Pr + Pv.

Power can be a scalar or a vector or both.

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