If you do something vacantly, it's characterized by a lack of feeling or expression. Nod along vacantly as your friend describes her weekend and she'll wonder if you're really paying attention.
The adverb vacantly is used for actions that have an underlying blankness to them. Vacant means "empty," and whenever you do something vacantly, it's empty of thought, expression, or emotion. After witnessing a tragedy, you might stare vacantly ahead, speechless. Exhausted from lack of sleep, you may find yourself gazing vacantly at a book without processing the words on the page.