# What is the angle between <-7,-9,-2> and < 2,-3,5>?

Dec 14, 2016

The angle is $= 87.7$º

#### Explanation:

The angle between 2 vectors is given by the dot product definition

veca.vecb=∥veca∥*∥vecb∥*costheta

The dot product is

〈-7,-9,-2〉.〈2,-3,5〉=((-7*2)+(-9*-3)+(-2*5))

$= - 14 + 27 - 10 = 3$

The modulus of veca=∥〈-7,-9,-2〉∥=sqrt(63+81+4)=sqrt144=12

The modulus of vecb=∥〈2,-3,5〉∥=sqrt(4+9+25)=sqrt38

Therefore,

costheta=(veca.vecb)/(∥veca∥*∥vecb∥)=3/(12sqrt38)=0.04

$\theta = 87.7$º