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For two radius vectors $r,r'$ we have in Cartesian coordinates $$\|r-r'\|_2 = \sqrt{(x-x')^2+(y-y')^2+(z-z')^2}$$. Is there a similar expression for this in terms of the components in cylindrical coordinates?

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  • $\begingroup$ no the general $r$ is meant not the one that is part of the coordinates itself. $\endgroup$
    – user66906
    May 5 '14 at 17:49
  • $\begingroup$ I see, I confused with the $r$ that is distance on $xy$ plane. $\endgroup$
    – Kaster
    May 5 '14 at 17:50
  • $\begingroup$ I think you just need to substitute $x = \rho \cos \phi, y = \rho \sin \phi$ and $z = z$ to your distance. Same for $x', y', z'$. $\endgroup$
    – Kaster
    May 5 '14 at 17:52
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If you are looking to find the distance between two points on cylindrical coordinate then it's $$\sqrt{r_1^2 + r_2^2 - 2 r_1 r_2 \cos (\theta_1 - \theta_2) + (z_1 - z_2)^2} $$

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