My first intuition is you couldn't really "add" vectors in (r,0) form in an addition format, since both the r and theta values of u and v when added don't really point to where this depicted cartesian-added vector (u+v) is pointing. Unless "adding vectors" meant something different, then you could add (r,0) arrows to create a result that describes something like the "cumulative radius" and "cumulative theta"?

My first intuition is you couldn't really "add" vectors in (r,0) form in an addition format, since both the r and theta values of u and v when added don't really point to where this depicted cartesian-added vector (u+v) is pointing. Unless "adding vectors" meant something different, then you could add (r,0) arrows to create a result that describes something like the "cumulative radius" and "cumulative theta"?