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I understand the the polar coordinate system without vectors. But when it is related to vector, it is confusing. Do the unit vectors r and phi keep changing?

How do I interpret it as they changes? For example, F = 2 r + 3 phi. Based on the vector addition and scale multiplication, it shall put 3 unit vectors phi to the head of 2 unit vectors r. But it seems it is wrong.

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# I Coordinate System

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