I was looking at this picture. I can't seem to get the right hand rule to work. I put my thumb on vector r and my index on vector F. My middle finger points INTO the page!
Don't just place your fingers over the vectors. Also make sure that your fingers point in the same direction as the vectors. It's OK to move the vectors around (as long as they don't turn or stretch/shrink) so that they start at the same spot. That might help since your fingers do start in a single spot (sort of) AKA your hand.