##### Position, Displacement and Separation Vectors
c.m.va.pds

Cartesian coordinates. Position vector:

\[ {\bf r} \equiv x ~\hat{\bf x} + y ~\hat{\bf y} + z ~\hat{\bf z} \label{Gr(1.19)} \]

Magnitude

\[ r = \left[ x^2 + y^2 + z^2 \right]^{1/2} \label{Gr(1.20)} \]

Unit radial vector:

\[ \hat{\bf r} = \frac{\bf r}{r} \label{Gr(1.21)} \]

Infinitesimal displacement vector:

\[ d{\bf l} = dx ~\hat{\bf x} + dy ~\hat{\bf y} + dz ~\hat{\bf z} \label{Gr(1.22)} \]

Separation vector: for two position vectors \({\bf r}_a, {\bf r}_b\),

\[ {\bf r}_{ab} \equiv {\bf r}_a - {\bf r}_b \label{Gr(1.23)NOT} \]

NOTE: I WILL NOT USE THE …ING GRIFFITHS CURLY \(r\) notation!

- it is ambiguous and non self-evident
- it is not standard, and I strongly discourage its use!
- it doesn't save time (proof: Griffiths keeps repeating it again and again)
- it is impossible to do reliably on the blackboard (especially with my handwriting!)
- when you speak, there is no difference between Griffiths' \(r\) and \(r\)!

Except where otherwise noted, all content is licensed under a Creative Commons Attribution 4.0 International License.

Author: Jean-Sébastien Caux

Created: 2022-03-24 Thu 08:42