Find a unit vector a which is horizontal and perpendicular to the vector b=4i -3j +7k.
if so, just make the z-coordinate zero. otherwise, we need the dot product of the vectors to be zero.
so the horizontal vector perpendicular to <a, b, c> is the vector <b, -a, 0>
so here, your vector would be, a = -3i - 4j
now find the unit vector in that direction