Question

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

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

Answer 1

Answer: (B)

$|\vec{a}|=2,|\vec{b}|=7$
$\vec{a}\times \vec{b}=3\hat{i}+2\hat{j}+6\hat{k}$
we know that $\vec{a}\times \vec{b}=|\vec{a}||\vec{b}|\sin \theta \hat{n}$
or $|\vec{a}\times \vec{b}|=||\vec{a}||\vec{b}|\sin \theta .\hat{n}|$
$\Rightarrow \sqrt{9+4+36}=|\vec{a}||\vec{b}||\sin \theta |.1$
$\Rightarrow \sqrt{49}=2\times 7|\sin \theta |$
$\Rightarrow \frac{1}{2}=\sin \theta \Rightarrow \theta =\frac{\pi }{6}$