So your working is incorrect. The negative sign in front of A (which really depends on your coordinate system anyway) is not there.
There are two ways to get the direction. One is the "right hand rule" (which I'll suggest you do a web search on) or simply work out the determinant:
Since your vectors are both in the xy plane (most people would choose +x in the E and +y in the N directions) your cross product will end up in the z direction. (I get the - z direction, to be precise.)