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Question

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

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Solution

Given that a.b = 0
Then, either |a| = 0 or |b| = 0 or ab (in case a and b are non-zero) and if a×b=0 then 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


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