→a⋅→b=0
Then,
(i) Either |→a|=0 or
|→b|=0, or →a⊥→b (in case →a
and →b are non-zero)
→a×→b=0
(ii)
Either |→a|=0 or |→b|=0, or →a∥→b (in case →a and →b are non-zero)
But, →a and →b cannot be perpendicular and parallel simultaneously.
Hence, |→a|=0 or |→b|=0.