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)._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Vom Wesen physikalischer Gesetze München 1993
Vorlesungen über Physik I München 2001