What was ulysses grant's goal at vicksburg?

Well,

One of the Union strategies was to control the Mississippi River.  At this point in the war, the Union had taken control of the entire Mississippi River minus Vicksburg.

Grant's goal at Vicksburg was to capture it, which would severely weaken the Confederacy, as it was now split in two.

It's most likely choice a, it makes the most sense in my opinion.