# Coordinate transformations Spherical to Cartesian

 P: 20 Hi, 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 $$E = E_r~\hat{r}+E_{\theta}~\hat{\theta}+E_{\phi}~\hat{\phi}$$. But I know only the cartesian coordinate from where it starts, say $$(x,y,z)$$ and I do not know where it ends. So I am unable to find angles $$\theta$$ and $$\phi$$ for computing the transformation matrix $$R$$ that transforms the vector $$E$$ to cartesian system. This $$R$$ is the usual matrix with sines and cosines of $$\theta$$ and $$\phi$$ and can be seen here. http://en.wikipedia.org/wiki/Vector_...al_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
 Sci Advisor HW Helper P: 4,300 What do you mean, you don't know where it ends? Isn't the (r, theta, phi) system relative to (x, y, z)?
P: 20
 Quote by CompuChip What do you mean, you don't know where it ends? Isn't the (r, theta, phi) system relative to (x, y, z)?
May be I am missing something very simple here. But I do not know the $$(r,~\theta,~\phi)$$ as well. I did try to do it that way though to start with.

All I know is the magnitudes in the $$\hat{r},~\hat{\theta}$$ and $$\hat{\phi}$$ directions and the starting point. And nothing else.

Can the $$(r,~\theta,~\phi)$$ be found out from the magnitudes in the $$\hat{r},~\hat{\theta}$$ and $$\hat{\phi}$$ ($$E_r,~E_{\theta},~E_{\phi}$$ as above)?

It can be really simple. But I cannot just think about it right.

 Sci Advisor HW Helper P: 4,300 Coordinate transformations Spherical to Cartesian Yes, you might be missing something or I might. But aren't the coordinate values simply the coefficients of the unit vectors? Like, in a Cartesian system you can write either (3, 0, -2) for the coordinates of a point, or you can describe it by a vector $3 \hat x + 0 \hat y - 2 \hat z$. When writing down a tuplet of numbers like (3, 0, -2), we are implicitly assuming that we have these three basis vectors $\hat x, \hat y, \hat z$ and we are using them to fix our point.
P: 20
 Quote by CompuChip Yes, you might be missing something or I might. But aren't the coordinate values simply the coefficients of the unit vectors? Like, in a Cartesian system you can write either (3, 0, -2) for the coordinates of a point, or you can describe it by a vector $3 \hat x + 0 \hat y - 2 \hat z$. When writing down a tuplet of numbers like (3, 0, -2), we are implicitly assuming that we have these three basis vectors $\hat x, \hat y, \hat z$ and we are using them to fix our point.
Thanks Compuchip. I got your point. So stupid of me. The (x,y,z) can be used to find theta, phi. My bad.
 Sci Advisor HW Helper P: 4,300 You're welcome. We all get confused sometimes.

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