I strongly recommend that you go back and read the problem again. What you have written makes no sense at all. You are given a vector in three dimensions but you are trying to do the problem in two dimensions. A two dimensional vector cannot be co-linear with a three dimensional vector. Also, the cross product has nothing to do with this problem. Two vectors are co-linear if and only if one is a multiple of the other.
You are asked to find B "on the xy plane" but you still have to have three dimesions- B= (x, y, 0) for some numbers, x and y. The vector AB, then, is (x-1, y-1, 1), not just (x-1, y-1). V was given as (1, 2, 3), NOT just (1, 2). Find x and y such that (x-1, y-1, 1)= k(1, 2, 3) for some k. Look at the third component to immediately determine what k must be. Then solve x-1=k, y-1= 2k for x and y.