Question

If $|\overrightarrow{a}|=2,|\overrightarrow{b}|=7$ and $\overrightarrow{a}\times \overrightarrow{b}=3\hat{i}+2\hat{j}+6\hat{k}$ then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{2}$
• D. $\frac{\pi }{4}$

Answer 1

Answer: (B)

$\frac{\pi }{6}$

$|\overrightarrow{a}|=2,|\overrightarrow{b}|=7$ and $\overrightarrow{a}\times \overrightarrow{b}=3\hat{i}+2\hat{j}+6\hat{k}$
$|\overrightarrow{a}\times \overrightarrow{b}|=|\overrightarrow{a}||\overrightarrow{b}|\sin \theta |\hat{n}|$
$\Rightarrow \sqrt{9+4+36}=2.7.\sin \theta .1$
$\Rightarrow \sqrt{49}=2.7\times \sin \theta$
$\Rightarrow 7=7.2\sin \theta$
$\Rightarrow \sin \theta =\frac{1}{2}$
$\Rightarrow \theta =\frac{\pi }{6}$