Is the position vector r=xi+yj+zk just r=rerin spherical coordinates?
Yes. Note however that, unlike in the Cartesian representation, we can't use that to tell us where the point is, because we first need to know where the point is to know what vector ##\mathbf e_r## is.
You can use your equation, r=xi+yj+zk, with
x = r sinθ cosφ
y = r sinθ sinΦ
z = r cosθ
to continue using Cartesian base vectors. Check out: http://www.ittc.ku.edu/~jstiles/220/handouts/The Position Vector.pdf
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