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Physics as taught in high school would say that work is a scalar quantity.

More sophisticated forms of physics would say that work done is a Quaternion, both a scalar and a vector.

Work is both

  • w= [0,F][0,D]=[ 0 - F.D, 0 + 0 + FxD] = [-F.D, FxD] = -F.D + FxD.

    -F.D = -FDcos(FD) is scalar work out, and

  • w= FxD= FDsin(FD) a vector called Torque.
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