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- Thread starter seang
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quasar987

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what's rx?

- #3

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Is is a component of the vector I am working to convert to cartesian coordinates.

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HallsofIvy

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[tex]x= \rho cos(\theta)sin(\phi)[/tex]

[tex]y= \rho sin(\theta)sin(\phi)[/tex]

[tex]z= \rho cos(\phi)[/tex]

[tex]\rho= \sqrt{x^2+ y^2+ z^2}[/tex]

[tex]\theta= arctan(\frac{y}{z})[/tex]

[tex]\phi= arctan(\frac{z}{\sqrt{x^2+y^2}})[/tex]

The x-component of a vector is just the x coordinate of the corresponding point.

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? That seems too easy.

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[tex] \vec S = (S_R, S_\theta, S_\phi) [/tex]

and cartesian,

[tex] \vec C = (C_x, C_y, C_z) [/itex]

Now if you want the x-component of [itex] \vec C [/itex] you use the dot product, [itex] \vec C \cdot \hat x [/itex], where [itex] \hat x = (1,0,0) [/itex] (in cartesian coordinates).

Now if you want the x-component of [itex] \vec S [/itex] you use the dot product, [itex] \vec S \cdot \hat x [/itex].

You need to express the unit vectors in the different coordinate system though. You can do this with geometry.

That makes it a little bit more difficult for you.

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