Question

If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=7$ and $\overrightarrow{a}\times \overrightarrow{b}=3\hat{i}+2\hat{j}+6\hat{k}$, then $(\overrightarrow{a},\overrightarrow{b})=$

• A. ${30}^0$
• B. ${60}^0$
• C. ${45}^0$
• D. ${75}^0$

Answer 1

The correct option is A ${30}^0$

$|\overrightarrow{a}\times \overrightarrow{b}|=7$
$\overrightarrow{a}\times \overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}|\sin Q$
(where $\theta$ is angle between $\overrightarrow{a}$ and $\overrightarrow{b})$
$7=7\times 2\times \sin Q$
$\sin Q=\frac{1}{2}$
$Q={30}^0$