Statement I : If dot product and cross product of A→  and B→ are zero, it implies that one of the vector A→ and B→ must be a null vector.Statement II : Null vector is a vector with zero magnitude.

A→.B→ = |A|→|B|→ cosθ = 0A→×B→ = |A|→|B|→ sinθ = 0If A→ and B→ are not null vectors then it follows that sinθ and cosθ both should be zero simultaneously. But it cannot be possible so it is essential that one of the vector must be null vector.