If #A = <2 ,-5 ,-8 >#, #B = <-9 ,4 ,-2 ># and #C=A-B#, what is the angle between A and C?

1 Answer
Nov 12, 2016

The angle is #56.1#º

Explanation:

Let's calculate #vecC=vecA-vecB=〈2,-5,-8〉-〈-9,4,-2〉@#
#=〈11,-9,-6〉#

To calculate the angle #theta# between the 2 vectors, we use the dot product definition.

#vecA.vecC=∥vecA∥*∥vecC∥*costheta#

The dot product is #vecA.vecC=〈2,-5,-8〉.〈11,-9,-2〉#
#=22+45+16=83#

The modulus of #vecA# = #∥vecA∥=∥〈2,-5,-8〉∥=sqrt(4+25+64)=sqrt93#

The modulus of #vecC# = #∥vecC∥=∥〈11,-9,-6〉∥=sqrt(121+81+36)=sqrt238#

#costheta=83/(sqrt93*sqrt238)=0.56#

#theta=56.1#º