what is the difference between (where were you at last week) and (where are you at last week)

"where were you last week?" is the right answer. and it's past tense. " where are you at last week" is the wrong sentence. the right way is "where are you?" ( at this moment) .

Both are wrong. You should write:- Where were you last week? (in past tense) Where are you this week? (in present tense)

where are you going? I'm going back home.