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I have been thinking about dimensional analysis with respect to computer systems. It has become obvious to me that to be meaningful such an analysis has to distinguish dot product from vector products. An area can be considered the cross product of vectors. The question that arose is "Can an angle be considered a vector". Let us consider rotating a vector from one line of action to another line of action. Such a rotation will occur around an axis which is orthogonal to both vectors just like a cross product. Furthermore an, just as an area can only be viewed accurately from a normal to the plane, so to can an angle only be viewed accurately from that axis of rotation.

If an angle was a vector defined in this way:

WorkDone = Torque . RotationalAngle

which is completely analoguous with:

WorkDone = Force . Displacement

Your comments are invited.