# What is the angle between <-7,0 ,4>  and < -1,5,0>?

Jan 16, 2017

The angle is $80.2$º

#### Explanation:

The angle is given by the dot product definition

veca.vecb=∥veca∥*∥vecb∥costheta

Where, $\theta$ is the angle between the 2 vectors
Here, we have

veca=〈-7,0,4〉

vecb=〈-1,5,0〉

The dot product is 〈-7,0,4〉.〈-1,5,0〉=7+0+0=7

The modulus of $\vec{a}$ is =∥〈-7,0,4〉∥=sqrt(49+0+16)=sqrt65

The modulus of $\vec{b}$ is =∥〈-1,5,0〉∥=sqrt(1+25+0)=sqrt26

Therefore,

costheta=(veca.vecb)/(∥veca∥*∥vecb∥)=7/(sqrt65*sqrt26)=0.17

$\theta = 80.2$º