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

Answer

`(-1)/(sqrt(6))hat(i)+(2)/(sqrt(6))hat(j)-(1)/(sqrt(6))hat(k)`