Etymology
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Words related to vacation

*eue- 
*euə-, Proto-Indo-European root meaning "to leave, abandon, give out," with derivatives meaning "abandoned, lacking, empty."

It forms all or part of: avoid; devastation; devoid; evacuate; evanescent; vacant; vacate; vacation; vacuity; vacuole; vacuous; vacuum; vain; vanish; vanity; vaunt; void; wane; want; wanton; waste.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit una- "deficient;" Avestan va- "lack," Persian vang "empty, poor;" Armenian unain "empty;" Latin vacare "to be empty," vastus "empty, waste," vanus "empty, void," figuratively "idle, fruitless;" Old English wanian "to lessen," wan "deficient;" Old Norse vanta "to lack."
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holiday (n.)
1500s, earlier haliday (c. 1200), from Old English haligdæg "holy day, consecrated day, religious anniversary; Sabbath," from halig "holy" (see holy) + dæg "day" (see day); in 14c. meaning both "religious festival" and "day of exemption from labor and recreation," but pronunciation and sense diverged 16c. As an adjective mid-15c. Happy holidays is from mid-19c., in British English, with reference to summer vacation from school. As a Christmastime greeting, by 1937, American English, in Camel cigarette ads.
staycation (n.)
also stay-cation, 2008, American English, a word from the "Great Recession" of that year, from stay (v.1) + ending from vacation.
vac 
1709 as a colloquial shortening of vacation (n.); 1942 as a colloquial shortening of vacuum (v.); 1974 as a colloquial shortening of vacuum cleaner.