(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the cartesian, cylindrical, spherical coordinate system,

prove that

[itex]\nabla[/itex].[itex]\vec{r}[/itex] = 3 and [itex]\nabla[/itex]x[itex]\vec{r}[/itex]=0

2. Relevant equations

For cylindrical coord system,

[itex]\vec{r}[/itex] = s[itex]\vec{s}[/itex] + z[itex]\vec{z}[/itex]

[itex]\nabla[/itex] = [itex]\vec{s}[/itex] [itex]\delta[/itex]/[itex]\delta[/itex]s + [itex]\vec{\varphi}[/itex][itex]\frac{1}{\varphi}[/itex][itex]\delta[/itex]/[itex]\delta[/itex][itex]\varphi[/itex] + [itex]\vec{z}[/itex] [itex]\delta[/itex]/[itex]\delta[/itex]z

3. The attempt at a solution

Hi guys, I managed to do the cartesian coord part, but I'm having trouble with the cylindrical/spherical parts. Using these 2 equations I tried to do a dot product but I'm getting a 2 instead. What am I doing wrongly here?

Please help.

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# Coordinate systems

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