What about:
Up (0.0, 1.0, 0.0)
Right (1.0, 0.0, 0.0)
Front (0.0, 0.0, 1.0)

And then just rotating them?
Or if you already have the front vector, it shouldnt be a problem to rotate some vector around it, problem here is just to choose one of the endless possible vectors...

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