If | → a | = 2, | → b | = 5 and | → a × → b | = 8, then | → a · → b...

We have, $\left|\overset{\to}{a}\right| = 2, \left|\overset{\to}{b}\right| = 5$

and \left|\overset{\to}{a} \times \overset{\to}{b}\right| = 8$</p><p>Now, \left|\overset{\to}{a} \times \overset{\to}{b}\right| = \left|\overset{\to}{a}\right|\left|\overset{\to}{b}\right|sin\theta = 8$

$⇒ sin\theta = \pm \dfrac{4}{5}$

$∴ \overset{\to}{a} \cdot \overset{\to}{b} = \left|\overset{\to}{a}\right|\left|\overset{\to}{b}\right|cos\theta$

$= 10 . \left(\pm \dfrac{3}{5}\right) = \pm 6$

$⇒ \left|\overset{\to}{a} \cdot \overset{\to}{b}\right| = 6 .</p>$