If → P = 3 ^ i + 3 ^ j + 2 ^ k and → Q = 4 ^ i + 3 ^ j + 2 . 5 ^ k...

Unit vector in the direction of \overset{\to}{P} \times \overset{\to}{Q}\text{is}\overset{^}{n} = \dfrac{\overset{\to}{P} \times \overset{\to}{Q}}{| \overset{\to}{P} \times \overset{\to}{Q} |}.

Here, \overset{\to}{P} \times \overset{\to}{Q} = \left|\begin{cases}\overset{^}{i} & \overset{^}{j} & \overset{^}{k} \\ 3 & \sqrt{3} & 2 \\ 4 & \sqrt{3} & 2 . 5\end{cases}\right| = \sqrt{3}\overset{^}{i}2 + \overset{^}{j}2 - \sqrt{3}\overset{^}{k}

And \left|\overset{\to}{P} \times \overset{\to}{Q}\right| = \sqrt{{\left(\dfrac{\sqrt{3}}{2}\right)}^{2} + {\left(\dfrac{1}{2}\right)}^{2} + {\left(\sqrt{3}\right)}^{2}} = \sqrt{4} = 2$</p><p>$⇒ \dfrac{\overset{\to}{P} \times \overset{\to}{Q}}{| \overset{\to}{P} \times \overset{\to}{Q} |} = \dfrac{1}{2}\left(\sqrt{3}\overset{^}{i}2 + \overset{^}{j}2 - \sqrt{3}\overset{^}{k}\right)$</p><p>$= \dfrac{1}{4} ( \sqrt{3}\overset{^}{i} + \overset{^}{j} - 2\sqrt{3}\overset{^}{k} ) ⇒ x = 4