Find a unit vector perpendicular to each of the vectors `vec(a) + vec(b) and vec (a)

Find a unit vector perpendicular to each of the vectors `vec(a) + vec(b) and vec (a) - vec(b) ` where `vec(a) = 3 hat (i) + 2 hat (j) + 2 hat (k) ` and ` vec(b) = hat (i) + 2 hat (j) - 2 hat (k) ` .