If you have no activity for a few minutes, you'll go 'offline' on the forums.. Meaning the little green (or red if you're invisible, for me) light next to your name will go grey.
In maths, they are positional offsets. So for example, if point A is (0, 2) and point B is (1, 4) then vector A-->B is 1i + 2j (in vector notation, that basically means (1, 2).
In programming (which you probably won't find on this JASS forum, vectors probably refers to the above) a vector is an unlimited array, or something. I'm not totally sure.
The forum software says we have 554 members online now. We did not have that many unique visitors the whole day today. Too many bots and the disconnect between the forum counts and the stats.