Question

If $\left|\begin{array}{c}\overline{a}\end{array}\right|=4,\left|\begin{array}{c}\overline{b}\end{array}\right|=2$ and angle between $\overline{a}$ and $\overline{b}$ is $\frac{\pi }{6}$, then $(|\overline{a}\times \overline{b}|{)}^2$ equals

• A. $48$
• B. $16$
• C. $\overline{a}$
• D. None of these

Answer 1

The correct option is B $16$

Using fact $(\overline{a}\times \overline{b}{)}^2$ $=a^2{b}^2-a^2{b}^2{\cos }^2\theta$
$=(4\times 2{)}^2-(4\times 2{)}^2{\cos }^2\frac{\pi }{6}$
$=64\times {\sin }^2\frac{\pi }{6}$

$=64\times \frac{1}{4}=16$