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shyta
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Homework Statement
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
Homework 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
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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