Let → a and → b be two vectors. Let | → a | = 1, | → b | = 4 and →...

Given,

$\overset{\to}{a}$and $\overset{\to}{b}$ be two vectors, where $| \overset{\to}{a} | = 1, | \overset{\to}{b} | = 4$ and $\overset{\to}{a} \cdot \overset{\to}{b} = 2$,

Now given, $\overset{\to}{c} = \left(2\overset{\to}{a} \times \overset{\to}{b}\right) - 3\overset{\to}{b}$

So, $\overset{\to}{b} \cdot \overset{\to}{c} = \overset{\to}{b} \cdot \left(2\overset{\to}{a} \times \overset{\to}{b}\right) - 3\overset{\to}{b} \cdot \overset{\to}{b}$

⇒ \overset{\to}{b} \cdot \overset{\to}{c} = - 3 | b{|}^{2} \left\{\text{as}\left[\begin{cases}\overset{\to}{b} & 2\overset{\to}{a} & \overset{\to}{b}\end{cases}\right] = 0\text{or}\overset{\to}{b} \cdot \left(2\overset{\to}{a} \times \overset{\to}{b}\right) = 0\right\}

$⇒ \overset{\to}{b} \cdot \overset{\to}{c} = - 48$