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Q6  Given that  \vec a . \vec b = 0 \: \:and \: \: \vec a \times \vec b = 0 and . What can you conclude about the vectors\vec a \: \:and \: \: \vec b ?

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Given in the question

\vec a . \vec b = 0 and \vec a \times \vec b = 0

When \vec a . \vec b = 0, either |\vec a| =0,\:or\: |\vec b|=0,\vec a\: and \:\vec b are perpendicular to each other

When \vec a \times \vec b = 0 either |\vec a| =0,\:or\: |\vec b|=0,\vec a\: and \:\vec bare parallel to each other

Since two vectors can never be both parallel and perpendicular at same time,we conclude that

|\vec a| =0\:or\: |\vec b|=0

Posted by

Pankaj Sanodiya

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