The cross product of A and B is perpendicular to both A and B.
A × B = (4i + 2j + 2k) × (4i - 4j + 8k)
A × B = 16 (i × i) - 16 (i × j) + 32 (i × k) + 8 (j × i) - 8 (j × j) + 16 (j × k) + 8 (k × i) - 8 (k × j) + 16 (k × k)
A × B = -16 (i × j) - 32 (k × i) - 8 (i × j) + 16 (j × k) + 8 (k × i) + 8 (j × k)
A × B = -16k - 32j - 8k + 16i + 8j + 8i
A × B = 24i - 24j - 24k
The magnitude of A × B is
||A × B|| = 24 ||i - j - k|| = 24√3
Dividing A × B by its magnitude gives a unit vector,
(A × B)/||A × B|| = 1/√3 (i - j - k)
