If $|\overrightarrow{\mathrm{a}}|=2,|\overrightarrow{\mathrm{b}}|=5$ and $|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=8$, then $|\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}|$ is equa to :
Correct Option: 1
$|\overrightarrow{\mathrm{a}}|=2,|\overrightarrow{\mathrm{b}}|=5$
$|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}}||\overrightarrow{\mathrm{b}}| \sin \theta=\pm 8$
$\sin \theta=\pm \frac{4}{5}$
$\therefore \vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta$
$=10 \cdot\left(\pm \frac{3}{5}\right)=\pm 6$
$|\vec{a} \cdot \vec{b}|=6$
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