It is found that |A + B| = |A|. This necessarily implies,

Solution: 

|A + B| = |A|

Squaring both the sides

|A+B|² = |A|²

|A|² + |B|² + 2.|A| |B| cosθ  = |A|² 

∴ |B|² + 2.|A| |B| cosθ = 0

2.|A| |B| cosθ = - |B|2 

|A| |B| cosθ = \(-\frac{|B|^2}{2|A|}\)

A.B = \(-\frac{|B|^2}{2|A|}\)

∴ A.B \(\leq \) 0 {A.B = 0 when B = 0}

Hence, the correct option is (4)