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Let the vectors a and b be such that , then is a unit vector, if the angle between is

Q11  Let the vectors \vec a \: \: and\: \: \vec b  be such that |\vec a| = 3 \: \: and\: \: |\vec b | = \frac{\sqrt 2 }{3} , then  \vec a \times \vec bis a unit vector, if the angle between is \vec a \: \:and \: \: \vec b 

        \\A ) \pi /6 \\\\ B ) \pi / 4 \\\\ C ) \pi / 3 \\\\ D ) \pi /2

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P Pankaj Sanodiya

Given in the question,

|\vec a| = 3 \: \: and\: \: |\vec b | = \frac{\sqrt 2 }{3}

As given \vec a \times \vec b  is a unit vector, which means,

|\vec a \times \vec b|=1

|\vec a| | \vec b|sin\theta=1

3*\frac{\sqrt{2}}{3}sin\theta=1

sin\theta=\frac{1}{\sqrt{2}}

\theta=\frac{\pi}{4}

Hence the angle between two vectors is \frac{\pi}{4}. Correct option is B.

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