Final answer:
The geometry of dark matter distribution in the vicinity of the Milky Way is best described as a near-spherical halo, which is supported by observations of the galaxy's mass and gravitational effects.
Step-by-step explanation:
We can ascertain several things about the distribution of dark matter in the vicinity of the Milky Way galaxy. The evidence indicates that the majority of the mass in the Milky Way, around 90%, consists of dark matter forming a halo around the visible parts of the galaxy. The dark matter halo seems to be almost spherical and extends to at least 200,000 light-years from the galactic center. This halo contains much more mass than that of the luminous matter and manifests its presence through the gravitational effects on the orbits of remote star clusters and dwarf galaxies associated with the Milky Way.
There is no evidence of a uniform density distribution of dark matter filling all space, as would be suggested by option 3. Concerning the distribution of dark matter, option 4 can be confidently rejected as the geometry, while not completely understood, is known to some extent—namely, that it forms a halo. The inner parts of the galaxy, near the Sun, contain only a negligible amount of dark matter relative to luminous matter, suggesting that dark matter does not form a lens-shaped disk akin to the galaxy's disk of stars. Therefore, evidence most strongly supports option 2, indicating that the dark matter around the Milky Way galaxy appears to be a spherical halo.