If I understand correctly your question, the vector space in which the rotation takes place is of dimension 2.

Consequently, I do not understand well what you mean when you say that you perform a rotation "around the x and y axis", because this part of your question seems to refer to a rotation in a 3D space.

To answer your question, should I consider the overall space be 2D (and forget about the x and y axis) or 3D?
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