# What is the angle between <-3,2,0>  and < 5,0,2 >?

Mar 19, 2016

$\theta = {\cos}^{-} 1 \left(- \frac{5}{14}\right) \approx 111$

#### Explanation:

We will use the definition of the dot product:
$\vec{{v}_{1}} \cdot \vec{{v}_{2}} = | \vec{{v}_{1}} | | \vec{{v}_{1}} | \cos \theta$
$\cos \theta = \frac{\vec{{v}_{1}} \cdot \vec{{v}_{2}}}{| \vec{{v}_{1}} | | \vec{{v}_{1}} |}$
Now substituting $\vec{{v}_{1}} = < - 3 , 2 , 0 >$ and $\vec{{v}_{2}} = < 5 , 0 , 2 >$

$\cos \theta = \frac{- 15 + 0 + 0}{\left({\left(- 3\right)}^{2} + {2}^{2}\right) \cdot \left({5}^{2} + {2}^{2}\right)} = - \frac{5}{14}$

$\theta = {\cos}^{-} 1 \left(- \frac{5}{14}\right) \approx {111}^{o}$