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

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From Wolfram Mathworld[1], we see the following relations:

Additionally, it has already been shown on the same page[1] that:

Now, we simply need to combine these relations together to obtain:

And hence:

As was to be demonstrated.

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