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# If $| \overrightarrow a | = 2, | \overrightarrow b | = 7 \: and \: \overrightarrow a$ x $\overrightarrow b=3\hat i + 2\hat j + 6\hat k$, find the angle between $\overrightarrow a \: and \: \overrightarrow b.$

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Toolbox:
• $\sin\theta=\large\frac{\overrightarrow a\times \overrightarrow b}{\mid\overrightarrow a\mid\mid\overrightarrow b\mid}$
Step 1:
Given : $\mid\overrightarrow a\mid=2,\mid \overrightarrow b\mid=7$
$\mid\overrightarrow a\times \overrightarrow b\mid=\sqrt{(3)^2+(2)^2+(6)^2}$
$\qquad\qquad= 7$
Step 2:
$\sin\theta=\large\frac{\overrightarrow a\times \overrightarrow b}{\mid\overrightarrow a\mid\mid\overrightarrow b\mid}$
$\qquad=\large\frac{7}{2\times 7}$
$\qquad=\large\frac{1}{2}$
$\theta=\sin^{-1}(\large\frac{1}{2})$
$\quad=\large\frac{\pi}{6}$
answered Nov 7, 2013