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My main concern concerns have been with [itex]\vec{dl}[/itex] (I've sometimes seen it written [itex]\vec{dr}[/itex]) and [itex]\vec{ds}[/itex]. I've encountered [itex]dl[/itex] as a scalar when doing line integrals but not as a vector. After much searching I was able to discover that the vector [itex]\vec{ds}[/itex] is equal to [itex]ds\mathbf{\hat{n}}[/itex] where n is the unit vector normal to the surface. But I've still not been able to find such a definition for [itex]\vec{dl}[/itex]. I would appreciate if anyone could shed some light on what this actually is.