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Vector/Feynman: any physical quantity associated with three numbers that transform like the components of a step in space is a vector. (i.e. invariant under rotation or shifting of the axis system).
An equation like
F = R
would thus be correct in any coordinate system if it is correct in one.
Vectors/Feynman: the fact that a physical relation can be expressed as a vector equation assures us that the relationship remains unchanged by a simple rotation of the coordinate system.
Vectors: e..g momentum, speed, force, acceleration.
We can represent force by arrows, because it has the same mathematical transformation properties as a "step in space". The step is then a selected unit of force.
For example, if we represent force by a length, we still need a constant k:
F = kr.
Important Point: after drawing the lines we no longer need the axes! ((s) If there are several lines, they are related to one another, which makes the axes superfluous).
Vom Wesen physikalischer Gesetze München 1993
Vorlesungen über Physik I München 2001