is the answer vector AB? or is it -AB?

The answer is as follows:

The vector would point from B to A, so I'd call it -AB.

The resultant vector would begin at B, traverse to E, thence to F and end at A. The magnitude would simply be the length of the segment between A and B, but vectors, unlike scalars, have direction as well as magnitude. To fully define the vector, the direction from B to A must also be included. Therefore the vector would be BA or -AB