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I will assume a vector in a plane - in two dimensions. The idea of polar coordinates is that the vector is expressed as its length, and an angle.

If you already have the vector in rectangular coordinates, i.e. the x and y components, most scientific calculators have a function that might be labelled R->P, to convert from rectangular coordinates to polar coordinates. Otherwise, use basic trigonometry - but using the specialized function is much faster, if your calculator has it.

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Q: How a vector can be expressed polar component?
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