Let | → a | = 2, | → b | = 3 and the angle between the vectors → a...

Given,

$| \overset{\to}{a} | = 2, | \overset{\to}{b} | = 3$ and the angle between the vectors $\overset{\to}{a}$ and $\overset{\to}{b}$ be $\dfrac{\pi}{4}$,

Now solving,

$| ( \overset{\to}{a} + 2\overset{\to}{b} ) \times ( 2\overset{\to}{a} - 3\overset{\to}{b} ) {|}^{2}$

$= | - 3 ( \overset{\to}{a} \times \overset{\to}{b} ) + 4 ( \overset{\to}{b} \times \overset{\to}{a} ) {|}^{2}$ \left\{\text{as}\overset{\to}{a} \times \overset{\to}{a} = 0 \text{ and } \overset{\to}{b} \times \overset{\to}{b} = 0\right\}$</p><p>$= | 7 ( \overset{\to}{b} \times \overset{\to}{a} ) {|}^{2}$\left\{as\overset{\to}{b}\times\overset{\to}{a} = - \overset{\to}{a}\times\overset{\to}{b}\right\}$

$= 49 | a{|}^{2} | b{|}^{2}\sin^{2}\dfrac{\pi}{4}$

$= 49 \times 4 \times 9 \times \dfrac{1}{2}$

$= 882$