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Find \( \overrightarrow a.\overrightarrow b\: if \: \overrightarrow a = 3\hat i - \hat j + 2\hat k\: and \: \overrightarrow b = 2\hat i + 3\hat j + 3\hat k\)

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  • $\hat i.\hat i=1$
  • $\hat j.\hat j=1$
  • $\hat k.\hat k=1$
$\overrightarrow a=3\hat i-\hat j+2\hat k$
$\overrightarrow b=2\hat i+3\hat j+3\hat k$
$\therefore \overrightarrow a.\overrightarrow b=(3\hat i-\hat j+2\hat k).(2\hat i+3\hat j+3\hat k)$
$\Rightarrow 6-3+6$
$\Rightarrow 9$
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