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Question

Given that ab=0 and a×b=0. What can you conclude about the vectors a and b?

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Solution

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

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