If → a · → b = 1, → b · → c = 2 and → c · → a = 3 , then the value...

We know that

$\overset{\to}{a} \times \left(\overset{\to}{b} \times \overset{\to}{c}\right)$, \overset{\to}{b} \times \left(\overset{\to}{c} \times \overset{\to}{a}\right)$and$\overset{\to}{c} \times\left(\overset{\to}{a} \times \overset{\to}{b}\right) are all coplanar as$\overset{\to}{a} \times \left(\overset{\to}{b} \times \overset{\to}{c}\right) + \overset{\to}{b} \times \left(\overset{\to}{c} \times \overset{\to}{a}\right)$ + \overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right) = \overset{\to}{0}$.</p><p>Also, the scalar triple product of$3$vectors which are coplanar is$0.</p><p>Hence, \left[\overset{\to}{a} \times \left(\overset{\to}{b} \times \overset{\to}{c}\right)\overset{\to}{b} \times \left(\overset{\to}{c} \times \overset{\to}{a}\right)\overset{\to}{c} \times \left(\overset{\to}{a} \times \overset{\to}{b}\right)\right] = 0