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Coordinate systems/Derivation of formulas/Spherical from Cartesian unit vectors

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From Wolfram Mathworld[1], we have the following relations for the unit vectors in a Spherical coordinate system:

Next, we need to change all the and to . We use the following relations, also available on the same page[1]:

Using these, we can find the following quantities:

Lastly, we simply need to substitute these relations into our first set of equations to obtain our desired result:

  1. 1.0 1.1 http://mathworld.wolfram.com/SphericalCoordinates.html