  The recent data on the polarization of vector meson at LEP show that the
vector mesons favor the helicity zero state. We calculate the helicity density
matrix of vector meson which contains a polarized fragmenting quark by adding
the spin of the fragmenting quark and that of the antiquark created in the
fragmentation. The data at LEP imply a significant polarization for the
antiquark in the opposite direction as that of the fragmenting quark. We extend
the calculations to other reactions and make predictions for vector mesons in
deeply inelastic lepton-nucleon scatterings and polarized $pp$ collisions.
