What is the angle between <-5,-3,6 > and <3,9,-9> ?

1 Answer
Mar 19, 2018

The angle is =151.3^@

Explanation:

The angle between 2 vectors, vecA and vecB is given by the dot product definition.

vecA.vecB=∥vecA∥*∥vecB∥costheta

Where theta is the angle between vecA and vecB

The dot product is

vecA.vecB=〈-5,-3,6〉.〈3,9,-9〉=-15-27-54=-96

The modulus of vecA= ∥〈-5,-3,6〉∥=sqrt(25+9+36)=sqrt70

The modulus of vecB= ∥〈3,9,-9〉∥=sqrt(9+81+81)=sqrt171

So,

costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-96/(sqrt70*sqrt171)=-0.877

theta=arccos(-0.877)=151.3^@