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I would like to transform a vector from Spherical to cartesian coordinate system. But the question is probably not that straight forward. :(

I have a vector say [tex]E = E_r~\hat{r}+E_{\theta}~\hat{\theta}+E_{\phi}~\hat{\phi}[/tex].

But I know only the cartesian coordinate from where it starts, say [tex](x,y,z)[/tex] and I do not know where it ends. So I am unable to find angles [tex]\theta[/tex] and [tex]\phi[/tex] for computing the transformation matrix [tex]R[/tex] that transforms the vector [tex]E[/tex] to cartesian system. This [tex]R[/tex] is the usual matrix with sines and cosines of [tex]\theta[/tex] and [tex]\phi[/tex] and can be seen here.

http://en.wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates

So how do I go about it. Is there even a way to do this. Once again this is not a homework question and is for a small project that I am doing. There aren't any homeworks at this time of the year. :)

Appreciate any form of help.

Kedar

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# Coordinate transformations Spherical to Cartesian

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