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  • I have a doubt, kindly clarify. - Vector Algebra - JEE Main-3

If \left | \vec{a} \right |=4,\left | \vec{b} \right |=2,  and the angle between \vec{a}\; \; and \; \; \vec{b} \; \; is \; \; \frac{\pi }{6}\; then\; \; (\vec{a}\times \vec{b} )^{2} is equal to

  • Option 1)

    48

  • Option 2)

    16

  • Option 3)

    \vec{a}

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we learnt in 

Vector Product of two vectors(cross product) -

If \vec{a} and \vec{b} are two vectors and \Theta is the angle between them , then \vec{a}\times \vec{b}=\left |\vec{a} \left | \right |\vec{b} \right |Sin\Theta \hat{n}

- wherein

\hat{n} is unit vector perpendicular to both \vec{a} \: and \: \vec{b}

 

 (\vec{a}\times \vec{b})^{2}\:=\:\left | \vec{a} \right |^{2}\:\left | \vec{b} \right |^{2}\:sin^{2}\frac{\pi }{6}

=4^{2}\times2^{2}\times (\frac{1}{2})^{2}=16


Option 1)

48

This option is incorrect.

Option 2)

16

This option is correct.

Option 3)

\vec{a}

This option is incorrect.

Option 4)

none of these

This option is incorrect.

Posted by

Aadil

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