If → a , → b , → c are three non-zero vectors and ^ n is a unit...

Given:

\overset{\to}{a} = \alpha\overset{\to}{b} - \overset{^}{n} where, $\alpha \ne 0$

⇒ \overset{\to}{a} \cdot \overset{\to}{c} = \alpha\left(\overset{\to}{b} \cdot \overset{\to}{c}\right) - \left(\overset{^}{n} \cdot \overset{\to}{c}\right)

$⇒ \overset{\to}{a} \cdot \overset{\to}{c} = 12\alpha - 0$

Since, \overset{^}{n} ⊥ \overset{\to}{c} ⇒ \left(\overset{^}{n} \cdot \overset{\to}{c}\right) = 0.

Now,

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

$⇒ \overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right) = 12\overset{\to}{a} - 12\alpha\overset{\to}{b}$

$⇒ \overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right) = 12\left(\overset{\to}{a} - \alpha\overset{\to}{b}\right)$

⇒ \overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right) = 12\left(- \overset{^}{n}\right)

⇒ \left|\overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right)\right| = \left|12\left(- \overset{^}{n}\right)\right|

⇒ \left|\overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right)\right| = 12\left|\left(- \overset{^}{n}\right)\right|

$⇒ \left|\overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right)\right| = 12$