How could I export a `VectorPlot3D` object to VTK format?

I wish to export a vector field created by Mathematica in a VTK format to visualize in Paraview. All I have are coordinates and vectors defined at each co-ordinate. 

I can't figure out how to use `Export` to do this. I keep getting the error message: `List cannot be exported to the VTK format`. 

I am able to reproduce [this stack exchange post][1] which is very related but of course this involves glyphs that I don't want since I would like to visualize the flow in different ways.

Thank you!



  [1]: https://mathematica.stackexchange.com/questions/113819/how-to-export-vtk-in-mathematica