Is power vector or scalar

Answer 1

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.

Answer 2

Work is a scalar quantity. For a constant force applied in a constant direction, it is equal to the dot product (also known as the inner product or the scalar product) of the force vector with the displacement vector. The result of taking the dot product is a scalar, not a vector. (That is, the multiplication sign you have in your definition of work is not an "ordinary" multiplication sign. "Ordinary" multiplication is not an operation that can be applied to two vectors.)

For a force that is not constant, or that is applied along a changing direction, the work is defined as the integral of the dot product (F(r) * dr), where dr is the infinitesimal displacement vector. The result is again a scalar quantity.

Because both work and time are scalar quantites, their quotient (power) is also a scalar.

Answer 3

It is a scalar quantity.