Question

$\overline{a}$ is perpendicular to both $\overline{b}$ and $\overline{c}$. The angle between $\overline{b}$ and $\overline{c}$ is $\frac{2\pi }{3}$. If $\left|\overline{a}\right|=2,\left|\overline{b}\right|=3,\left|\overline{c}\right|=4$, then $\overline{c}.(\overline{a}\times \overline{b})=$

• A. $18\sqrt{3}$
• B. $12\sqrt{3}$
• C. $8\sqrt{3}$
• D. $6\sqrt{3}$

Answer 1

The correct option is B $12\sqrt{3}$

$c.(a$ x $b)=a.(b$ x $c)=a.(|b|$.$|c|sin{120}^o)=|c||a||b|sin{120}^o=2\times 3\times 4\times \frac{\sqrt{3}}{2}=12\sqrt{3}$