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^@#