Let vector a = i + j + √2k, vector b = b_{1}i + b_{2}j + √2k and vector c = 5i + j + √2k be three vectors such that the projection vector of vector b on vector a is vector a. If vector a + vector b is perpendicular to vector c, then |vector b| is equal to :

(1) √32

(2) 6

(3) √22

(4) 4