Question

If a.a = 0 and a.b = 0, then what can be conclude about the vector b?

Answer 1

It is given that a.a = 0 or $|a{|}^2=0\Rightarrow |a|=0\Rightarrow a=0$ i.e., a is a zero vector because its magnitude is zero.

Hence, a.b = 0 whatever b may ($\because$ a = 0). This means that nothing can be concluded about b, it can be any vector.