(a) If B =0 then $\phi = \mathbf{B.A} = 0.if\ \phi = 0\ then\ \phi = \mathbf{B}.\mathbf{A} = 0,\ \mathbf{B}$ may or may not be zero because angle between B and A may be 90${^\circ}.$
For same part $\phi$ may be positive and for remaining part, it may be negative so that the resultant $\phi$ becomes zero but B is non-zero.