Question

If the vector a is perpendicular to b and c, |a|=2, |b|=3, |c|=4 and the angle between b and c is $\frac{2\pi }{3}$ then |[a b c ]| =

• A. 24
• B. 12
• C. $12\sqrt{3}$
• D. $24\sqrt{3}$

Answer 1

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

$|\left[abc\right]|=|a.(b\times c)|=|a||b\times c\left||cos\right(a,b\times c)|=|a||b\times c|=|a||b|c|sin(b,c)$
$=\mathrm{2.3.4}sin\left(\frac{2\pi }{3}\right)=24.\frac{\sqrt{3}}{2}=12\sqrt{3}$.