If #A = <4 ,1 ,5 >#, #B = <6 ,2 ,-2 ># and #C=A-B#, what is the angle between A and C?

1 Answer
Nov 19, 2017

The angle is #=68.2^@#

Explanation:

The angle between #vecA# and #vecC# is given by the dot product definition.

#vecA.vecC=∥vecA∥*∥vecC∥costheta#

Where #theta# is the angle between #vecA# and #vecC#

The dot product is

#vecA.vecC=〈4,1,5〉.〈6,2,-2〉=24+2-10=16#

The modulus of #vecA#= #∥〈4,1,5〉∥=sqrt(16+1+25)=sqrt42#

The modulus of #vecC#= #∥〈6,2,-2〉∥=sqrt(36+4+4)=sqrt44#

So,

#costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=16/(sqrt42*sqrt44)=0.37#

#theta=68.2^@#