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I am trying to understand why work is a scalar, without knowing ahead of time that work is defined as:

[itex]W_{ab} = \int ^{\vec{r_{b}}}_{\vec{r_{a}}} \vec{F} \cdot d{\vec{r}}[/itex]

Essentially, I am trying to understand how this definition was derived (based on the one-dimensional work-energy theorem, which is easy to figure out).

[itex]W_{ab} = \int ^{\vec{r_{b}}}_{\vec{r_{a}}} \vec{F} \cdot d{\vec{r}}[/itex]

Essentially, I am trying to understand how this definition was derived (based on the one-dimensional work-energy theorem, which is easy to figure out).

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