# How do you find the angel between u=<-6,-2> and v=<2,12>?

##### 1 Answer
Nov 21, 2016

The angle is $117.9$º

#### Explanation:

The angle is given by the dot product definition

vecu.vecv=∥vecu∥*∥vecv∥*costheta

Where $\theta$ is the angle between the 2 vectors.

The dot prduct is vecu.vecv =〈-6,-2〉.〈2,12〉=(-12-24)=-36

The modulus of vecu=∥〈-6,-2〉∥=sqrt(34+4)=sqrt40

The modulus of vecv=∥〈2,12〉∥=sqrt(4+144)=sqrt148

Therefore, costheta=vecu.vecv/(∥vecu∥*∥vecv∥)

$= - \frac{36}{\sqrt{40} \cdot \sqrt{148}} = - 0.47$

$\theta = 117.9$º