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# If A = <5 ,4 ,8 >, B = <2 ,-7 ,6 > and C=A-B, what is the angle between A and C?

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#### Explanation

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#### Explanation:

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1
Jun 18, 2018

$\theta = \arccos \frac{75}{\sqrt{14070}}$

#### Explanation:

$C = \left(\begin{matrix}3 \\ 11 \\ 2\end{matrix}\right) , A = \left(\begin{matrix}5 \\ 4 \\ 8\end{matrix}\right)$

$A \cdot C = | A | \cdot | C | \cdot \cos \theta$

$\cos \theta = \frac{15 + 44 + 16}{\sqrt{25 + 16 + 64} \sqrt{9 + 121 + 4}}$

$\cos \theta = \frac{75}{\sqrt{3 \cdot 5 \cdot 7 \cdot 2 \cdot 67}}$

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