Question: Can these vector space examples be explained?

The uploaded worksheet contains two examples of the use of VectorCalculus[VectorSpace]. The first example seems explicable but the second does not.

I have tried and failed to find a full, clear explanation of how a vector describing a simple vector, spacecurve, or surface in the default vector space is transformed to appear in a user defined vector space.

Can anyone direct me to such an explanation, so that I can understand Maple's processing within the uploaded worksheet and enable me to use this Maple feature to future advantage?

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