Find the angle between two vectors i - 2 j + 3 k and 3 i - 2 j + … - Vidyadip

Question

Find the angle between two vectors $\hat i - 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k\;$

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Answer

$\overrightarrow a = \widehat i - 2\widehat j + 3\widehat k,\overrightarrow b = 3\widehat i - 2\widehat j + \widehat k \Rightarrow \left| {\overrightarrow a } \right| = \sqrt {14} ,\left| {\overrightarrow b } \right| = \sqrt {14} ,\overrightarrow a .\overrightarrow b = 10, $

$ \Rightarrow \frac{{\overrightarrow a .\overrightarrow b }}{{\left| {\overrightarrow a } \right|\left| {\overrightarrow b } \right|}} = \cos \theta \Rightarrow \frac{{10}}{{14}} = \cos \theta $

$\Rightarrow \cos \theta = \frac{5}{7} \Rightarrow \theta = {\cos ^{ - 1}}\frac{5}{7} \\\\\\ $

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