  We study the vortex-bright solitons in a quasi-two-dimensional
spin-orbit-coupled (SO-coupled) hyperfine spin-1 three-component Bose-Einstein
condensate (BEC) using variational method and numerical solution of a
mean-field model. The ground state of these vortex-bright solitons is radially
symmetric for weak ferromagnetic and polar interactions. For a sufficiently
strong ferromagnetic interaction, we observe the emergence of an asymmetric
vortex-bright soliton as the ground state. We also numerically investigate
stable moving solitons and binary collision between them. The present
mean-field model is not Galilean invariant, and we use a Galilean-transformed
model for generating the moving solitons. At low velocities, the head-on
collision between two {\em in-phase} solitons results either in collapse or
fusion of the soliton pair. On the other hand, in head-on collision, the two
{\em out-of-phase} solitons strongly repel each other and trace back their
trajectories before the actual collision. At low velocities, in a collision
with an impact parameter, the {\em out-of-phase} solitons get deflected from
their original trajectory like two rigid classical disks. These {\em
out-of-phase solitons} behave like classical disks, and their collision
dynamics is governed by classical laws of motion. However, at large velocities
two SO-coupled spinor solitons, irrespective of phase difference, can pass
through each other in a head-on collision like two quantum solitons.
