If |a|=2,|b|=5 and |a b|=8, then |a b| is equal to : - Vidyadip

Question

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

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Answer

c
$|\vec{a}|=2,|\vec{b}|=5$

$|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta=\pm 8$

$\sin \theta=\pm \frac{4}{5}$

$\therefore \vec{a} \cdot \vec{b}=|\vec{a}| \vec{b} \mid \cos \theta$

$=10 \cdot\left(\pm \frac{3}{5}\right)=\pm 6$

$|\vec{a} \cdot \vec{b}|=6$

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