Find a Unit Vector Perpendicular to Each of the Vectors a + B and a B , Where a = 3 ^ I + 2 ^ J + 2 ^ K and B = ^ I + 2 ^ J 2 ^ K .

Question

Find a unit vector perpendicular to each of the vectors [\vec{a} + \vec{b} \text{ and } \vec{a} - \vec{b} , \text{ where } \vec{a} = 3 \hat{ i } + 2 \hat{ j } + 2 \hat{ k } \text{ and } \vec{b} = \hat{ i } + 2 \hat{ j } - 2 \hat{ k } .]