Vectors Question using Calculus -- Swimmer crossing a River

[etotheipi]

Relative meaning in the direction of.

I know this is an old thread, but this just bothered me. Relative to does not mean 'in the direction of', relative to implies a subtraction i.e. 'from the perspective of'. A part of a vector in a certain direction is something different, i.e. a vector component / vector projection.