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Work is the product of Force F and Displacement D. Work is a vector when the angle between the force and the displacement is not a multiple of 180 degrees.

FD = -F.D + FxD = [0,F][0,D]= [0 -F.D,0D + 0F + FxD] =[-F.D, FxD]

-F.D= -FDcos(FD) is called scalar Work. FxD = FDsin(FD is called Torque, a vector.

Work is a quaternion quantity. A quaternion is the sum of a scalar and three vectors. Most quantities are quaternions, the sum of a scalar and three vectors.

F= [Fs.Fd] D=[Ds,Dv] where Fs and Ds are scalar forces and distance.

Work W = FD = [FsDs - Fd.Dv, FsDv + FdDs + FdxDv]

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