cross product for multi concentric vector (cylindrical coordinates)

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Hi Guys,
I have created multi vectors in cylindrical coordinates, as seen in the attached images, I need to make a cross product between the centeral position vector by all position vector for each plane, an so on, pls help something like:
cross(0,0,z(1)), (x(1), y(1), z(1))
also I need to quiver all resulted vectors

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