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
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
Updated On: Jun 21, 2022
- $ \frac{\pi}{3} $
- $ \frac{\pi}{6} $
- $ \frac{\pi}{2} $
- $ \frac{\pi}{4} $
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The Correct Option is B
Solution and Explanation
$|\vec{a} | = 2 , |\vec{b}| = 7$
$\vec{a} \times \vec{b} = 3 \hat{i} + 2 \hat{j} + 6\hat{k}$
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|$
$\Rightarrow\:\: \frac{1}{2} = \sin \theta \Rightarrow \:\:\: \theta = \frac{\pi}{6}$
$\vec{a} \times \vec{b} = 3 \hat{i} + 2 \hat{j} + 6\hat{k}$
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|$
$\Rightarrow\:\: \frac{1}{2} = \sin \theta \Rightarrow \:\:\: \theta = \frac{\pi}{6}$
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