# What is the angle between <-2,3,1>  and < 4,1,4 >?

Jan 3, 2017

The answer is $= 92.7$º

#### Explanation:

We use the dot product definition to calculate the angle $\theta$ between 2 vectors,

veca.vecb=∥veca∥*∥vecb∥*cos theta

cos theta=(veca.vecb)/(∥veca∥*∥vecb∥)

We start by calculating the dot product,

veca:vecb=〈-2,3,1〉*〈4,1,4〉=(-8+3+4)=-1

The modulus of veca=∥〈-2,3,1〉∥=sqrt(4+9+1)=sqrt14

The modulus of vecb=∥〈4,1,4〉∥=sqrt(16+1+16)=sqrt33

$\cos \theta = - \frac{1}{\sqrt{14} \cdot \sqrt{33}} = - 0.465$

$\theta = 92.7$º