  The vortex configurations in the Bose-Einstein condensate of the mixture of
two different spin states |F=1,m_f=-1> and |2,1> of ^{87}Rb atoms corresponding
to the recent experiments by Matthews et. al. (Phys. Rev. Lett. 83, 2498
(1999)) are considered in the framework of the Thomas-Fermi approximation as
functions of N_2/N_1, where N_1 is the number of atoms in the state |1,-1> and
N_2 - in the state |2,1>. It is shown that for nonrotating condensates the
configuration with the |1,-1> fluid forming the shell about the |2,1> fluid
(configuration "a") has lower energy than the opposite configuration
(configuration "b") for all values of N_2/N_1. When the |1,-1> fluid has net
angular momentum and forms an equatorial ring around the resting central
condensate |2,1>, the total energy of the system is higher than the ground
energy, but the configuration "a" has lower energy than the configuration "b"
for all N_2/N_1. On the other hand, when the |2> fluid has the net angular
momentum, for the lowest value of the angular momentum \hbar l (l=1) there is
the range of the ratio N_2/N_1 where the configuration "b" has lower energy
than the configuration "a". For higher values of the angular momentum the
configuration "b" is stable for all values of N_2/N_1.
