What of the following military strategies allowed the union to gain control of Vicksburg?

The Union's successful military strategy to gain control of Vicksburg involved a combination of a prolonged siege and strategic maneuvering. General Ulysses S. Grant encircled the city, cutting off supplies and reinforcements while bombarding it to weaken Confederate defenses. This approach, along with the diversion of Confederate forces elsewhere, ultimately forced the surrender of Vicksburg on July 4, 1863, giving the Union control of the Mississippi River and splitting the Confederacy.