What vessels sustain a drop in pressure from approximately 35 mm hg to around 17 mm hg?

The correct answer is capillary.

The force that drives fluid out of capillaries and into the tissues is called capillary hydrostatic pressure (CHP) and it rises as the fluid (blood) moves into tissues. CHP may drop along the length of the capillary by 17-35 mmHg and it is highest at the arteriolar end of the capillary and lowest at the venular end.