I believe that "vacation" has the same roots as "vacate". In any case, I use "vac." and "vacation" because that's how the periods are listed in the Oxford University Pocket Diary, and I just try to go along with local customs[1], unless there is very good reason not to do so. In the diary the main divisions of the year are Michaelmas Term, Christmas Vacation, Hilary Term, Easter Vacation, Trinity Term and Long Vacation. I take it that "vacation" is used because the students vacate the colleges.
Best wishes,
Bob
PS I did a bit more investigation, and here's what Wikipedia has to say.
http://en.wikipedia.org/wiki/VacationIn the United Kingdom, vacation once specifically referred to the long summer break taken by the law courts and, later, universities—a custom introduced by William the Conqueror from Normandy where it facilitated the grape harvest. In the past, many upper-class families moved to a summer home for part of the year, leaving their usual family home vacant.
RLF
PPS [1] There is more than one way to skin a cat, not that I'm particularly into cat skinning.
RLF