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  4. If | veca|=2,| vecb|=5 and | veca × vecb|=8, then | veca ⋅ vecb| is equal to :

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Q. If $|\vec{a}|=2,|\vec{b}|=5$ and $|\vec{a} \times \vec{b}|=8$, then $|\vec{a} \cdot \vec{b}|$ is equal to :

JEE MainJEE Main 2021Vector Algebra

Solution:

$|\vec{a}|=2,|\vec{b}|=5$
$|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta=\pm 8$
$\sin \theta=\pm \frac{4}{5} \therefore \vec{a} \cdot b v=|\vec{a}||\vec{b}| \cos \theta$
$=10 \cdot\left(\pm \frac{3}{5}\right)=\pm 6$
$|\vec{a} \cdot \vec{b}|=6$