If so, what vector does it signify?
PS: $R =$ is the radial distance of the vector $\mathbf R$.
2026-03-27 00:10:52.1774570252
Can $\mathbf R$ be negative in spherical coordinate system?
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No, $r$ shouldn't be negative. If it is for some reason, you restore a positive value with
$$r,\theta,\phi\leftrightarrow-r,-\theta,\pi-\phi$$
following the convention in https://en.wikipedia.org/wiki/Spherical_coordinate_system.