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

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  • For two vectors $ \overrightarrow a \: and \: \overrightarrow b$, the vector product $ \overrightarrow a$ x $ \overrightarrow b=|\overrightarrow a||\overrightarrow b| \sin \theta \hat n$ with $ \hat n \perp $ to $ \overrightarrow a \: and \: \overrightarrow b\: and \: \overrightarrow a, \overrightarrow b, \hat n$ forming a right handed system.
$ | \overrightarrow a \times \overrightarrow b| = |\overrightarrow a||\overrightarrow b| \sin \theta$
$ \sqrt{9+4+36} = (2)(7) \sin \theta$
$ 7 = 14 \sin \theta \Rightarrow \sin \theta = \large\frac{1}{2}$
$ \theta = \sin^{-1} \large\frac{1}{2} \: \: \therefore \theta = \large\frac{\pi}{6} \: or \: \large\frac{5\pi}{6}$
answered Jun 5, 2013 by thanvigandhi_1
 

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