Since you've not defined what $U$ and $V$ mean, I can't answer any further than that. This Python program calculates Cartesian product of two sets.Cartesian product is also known as Cross product. Now $\hat r$ is the direction that $\vec p$ changes when $r$ increases, and $\hat \theta$ is the direction that $\vec p$ changes then $\theta$ increases: Python Program To Find Cartesian (Cross) Product Of 2 List. Letting $\vec p = x\hat i y \hat j$ be the position vector, and noting that $x = r\cos \theta, y = r\sin \theta$, we have $$\vec p = r\cos \theta \hat i r\sin \theta\hat j$$. $\vec v = v_r \hat r v_\theta \hat \theta$, where $\hat r$ and $\hat \theta$ are the unit radial vector and unit rotational vector at $(r, \theta)$.
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