State vectors of "interesting" multiple stars
The USNO Sixth Catalog of Orbits of Visual Binary Stars (ORB6)
has the orbital elements you need.


$\gamma$ And is WDS 02039+4220
$\alpha$ Gem is WDS 07346+3153
$\zeta$ UMa is WDS 13239+5456


Double star expert Bruce MacEvoy explains orbital elements in maybe enough detail to help you work out some state vectors.
My search also turned up a book chapter by Andreas Alzner.