Let a = 3i + 2j + 2k and b = i + 2j - 2k be two vectors. If a vector perpendicular to both the vectors a + b and a - b has the magnitude 12, then one such vector is?

Correct option is C. 4(2i - 2j - k)
(a + b) x (a - b) = 2(b x a) = 2|i j k
1 2 -2
3 2 2| = 2(8i - 8j + 4k)
Required vector = ±12(2i - 2j - k)/3 = ±4(2i - 2j - k).