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We know that vector quantities follow vector law of addition and vector addition only makes sense in a plane/space (we can treat vector addition in a line as scalar addition). It is also worth noting that velocity tells tells how the location is changing or towards which direction the object is getting directed and force tells us how location of an object will change or is changing with some particular effort applied.

So, is it safe to say that vector quantities always have something to do with location?

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  • $\begingroup$ A vector quantity has to do with how it changes under rotations and reflections of the coordinate system. $\endgroup$ – Diracology Jul 9 '17 at 14:14
  • $\begingroup$ @Diracology and coordinate system has to do with location, right? $\endgroup$ – ankit Jul 9 '17 at 14:16
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    $\begingroup$ What about magnetic field? $\endgroup$ – probably_someone Jul 9 '17 at 14:32
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    $\begingroup$ A counterexample: A momentum vector $p_{\mu}$ has nothing to do with location $x^{\nu}$. $\endgroup$ – Qmechanic Jul 9 '17 at 14:43
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    $\begingroup$ A better way to look at this is that any space of vectors, such as the space of magnetic field vectors, has the same structure as the space of displacement vectors. "Same structure" means that they transform in the same way under a change of coordinates. $\endgroup$ – Ben Crowell Jul 9 '17 at 15:31

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