If you have a force vector and motion along some line other than this, then you can either use vector math or you can do it longhand, e.g. diagonal of the rhomboid and replace the vector with the scalar of d*f. Thus there is nothing absolutely requiring that we define force as acting along the line of motion, it's just a convention, or IOW, another method of solution. In the former case the force doesn't act along the line, only a component of it does. How is the operator thus distinct from the cross product in your r x f ? You are changing conventions from one equation to the other and thus comparing apples and oranges. Your argument about the difference between torque and energy is invalid. If the entire problem were worked out in vector format then the only difference, dimensionally, between the two terms would be the inclusion of radians in the torque expression to make them equal, i.e. to convert them into each other in a rotational system, as pointed out by Don Gilmore. More specifically some angular velocity reference must be supplied. It isn't the cross product that separates these terms from each other, it is the non-equivalence of the dimensionality of r and d. The radian should not be dimensionless.
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