If #A = <5 ,6 ,-3 >#, #B = <-9 ,6 ,-5 ># and #C=A-B#, what is the angle between A and C?

1 Answer
Nov 14, 2016

The angle is #=57.3#º

Explanation:

Let's start calculating #vecC#

#vecC=vecA-VecB=〈5,6,-3〉-〈-9,6,-5〉#
#=〈14,0,2〉#

To calculate the angle #theta# between #vecA# and #vecC#,
we use the dot product definition:

#vecA.vecC=∥vecA∥*∥vecC∥costheta#

The dot product #=〈5,6,-3〉.〈14,0,2〉=70+0-6=64#

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

The modulus of #vecC=∥〈14,0,2〉∥=sqrt(196+0+4)=sqrt200#

#:. cos theta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=64/(sqrt70sqrt200)#

#costheta=0.54#

#theta=57.3#º