# If A = <3 ,-1 ,3 >, B = <2 ,-3 ,5 > and C=A-B, what is the angle between A and C?

Nov 20, 2016

${112.47}^{0}$

#### Explanation:

C= A-B= <3,-1,3>- <2, -3, 5> = < 1,2,-2>

Angle between A and C would be given by $\cos \theta = \frac{A \cdot C}{| A | | C |}$

$\cos \theta = \frac{3 \cdot 1 + \left(- 1\right) \cdot 2 + 3 \left(- 2\right)}{\sqrt{{3}^{2} + {\left(- 1\right)}^{2} + {3}^{2}} \sqrt{{1}^{2} + {2}^{2} + {\left(- 2\right)}^{2}}}$

=$- \frac{5}{\sqrt{19} \sqrt{9}}$= -0.3823

$\theta = \arccos - 0.3823$ =${112.47}^{0}$