What is the radius vector of a material point?

A vector drawn from the origin to a point within any coordinate system (fixed or not) can be defined as the position vector for that point in that system. The coordinates for the point depend on how the system is defined. If you are going from a (2D) polar to a rectangular Cartesian system, then x = R cos(θ) and y = R sin(θ), where θ is measured from the x axis to R.