  We propose a new model for the origin and evolution of the Local Group of
Galaxies (LGG) which naturally explains the formation of the Magellanic Clouds
and their large orbital angular momenta around the Galaxy. The basic idea is
that an off-center hydrodynamical collision occurred some 10 Gyr ago between
the primordial gas-rich Andromeda galaxy and the similar Galaxy, and compressed
the halo gas to form the LGG dwarf galaxies including the Magellanic Clouds. In
this model, new-born dwarf galaxies can be expected to locate near the orbital
plane of these two massive galaxies. In order to see the reality of this model,
we reexamine the two-dimensional sky distribution of the LGG members and the
Magellanic Stream, we confirm an earlier and widely-discussed idea that they
align along two similar great circles, each with an angular width of $\sim
30^{\circ}$, and the planes of these circles are approximately normal to the
line joining the present position of the sun and the Galactic center. Further
we make a three-dimensional distribution map of these objects, and observe it
from various directions. A well-defined plane of finite thickness is found,
within which most of the member galaxies are confined, supporting the existence
of the above circles on the sky. Thus we could determine the orbital elements
of M31 relative to the Galaxy through reproducing the well-studied dynamics of
the LMC and the SMC around the Galaxy. The expected proper motion of M31 is
$(\mu_l, \mu_b)=(38 \mu as/yr, -49 \mu as/yr)$. Probable orbital motions of the
other dwarfs are also determined, and the corresponding proper motion for each
object is given to compare with observations in near future.
