Question

If $|\overrightarrow{a}|=4,|\overrightarrow{b}|=2$ and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $\frac{\pi }{6}$. Then $|\overrightarrow{a}\times \overrightarrow{b}{|}^2$ is equal to ?

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

Answer 1

Answer: (B)

$16$

By property:
$|\overrightarrow{a}\times \overrightarrow{b}|=|\overrightarrow{a}||\overrightarrow{b}|\sin \theta =4\cdot 2\sin \frac{\pi }{6}=4$
$\therefore |\overrightarrow{a}\times \overrightarrow{b}{|}^2=16$