vac

The whole family starts from one simple Latin picture: a space with nothing in it. The verb vacāre meant "to be empty, to be free," and the adjective vacuus meant "empty." From that single image of emptiness, the root branched into four spelling families, each pushing the idea of "empty" in a slightly different direction.

vac- / vacu- keeps the meaning the most literal. A room with nobody in it is vacant; the empty slot it leaves is a vacancy. To vacate a place is to make it empty by leaving. A vacuum is the purest case — a space emptied even of air. And vacation is the surprise of the group: it literally means "being emptied of duties." When the law courts of old Europe emptied out for the season, that empty stretch of time became your holiday. To evacuate (e- "out" + vacāre) is to empty a place out, usually in a hurry — clearing people away from danger.

van- / vain- is the same root worn down through French, and here "empty" turns figurative. Something vain is empty of substance: effort that is vain produces nothing, and a person who is vain is puffed up over nothing. Vanity is that emptiness dressed up as pride. And vanish is the most vivid of all — to vanish is to become empty, to leave nothing behind where something just was.

void- came through Old French voide and carries "empty" into the realm of nothingness and nullity. A void is empty space — and to declare a contract void is to empty it of all force, to make it count for nothing. To avoid something is, originally, to empty yourself away from it — to make it absent from your path. To be devoid of something (de- intensifying) is to be utterly empty of it.

The pattern to hold onto: every member, no matter how it is spelled, is some shade of empty. vac-/vacu- = physically empty (vacant, vacuum, vacation, evacuate); van-/vain- = empty of worth or substance, fading into nothing (vain, vanity, vanish); void- = empty meaning invalid or kept-away (void, avoid, devoid).