Vacantly adv. : In a vacant manner; inanely.

Example:
When was the last time you stared Vacantly off into space? And why?

Taxonomy
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Defination from the web:
Vacantly in the Online Dictionary. Meaning of Vacantly. Pronunciation of Vacantly. Translations of Vacantly. Vacantly synonyms, Vacantly antonyms. ... As soon as his chattering teeth would let him speak, he smiled vacantly, and said he thought it must have been the Cramp. ...