My textbook reports the following definition of Work:
where ds is the infinitesimal displacement.
I know that an infinitesimal displacement is usually denoted by dr and I also know that the magnitude of dr is given by ds (infinitesimal distance) Now, if we are talking about displacement (in Work definition), why should we use ds instead of dr?
I ask this because my textbook always refers to infinitesimal displacement as dr. I have always associated 's' to distance, so I see ds as an infinitesimal "distance vector", but I am quite sure that distance is only a scalar quantity, not a vector.