If #A = <6 ,8 ,2 >#, #B = <7 ,1 ,-4 ># and #C=A-B#, what is the angle between A and C?

1 Answer
Nov 22, 2016

THe angle is #49#º

Explanation:

Let's start by calculating #vecC#

#vecC=vecA-vecB=〈6,8,2〉-〈7,1,-4〉=〈-1,7,6〉#

The angle between 2 vectors is given by the dot product.

#vecA.vecC=∥vecA∥*∥vecC∥*costheta#

where, #theta# is the angle between the two vectors.

The dot product is
#=〈-1,7,6〉.〈6,8,2〉=-6+56+12=62#

The modulus of #vecA# is

#∥vecA∥=∥〈6,8,2〉∥=sqrt(36+64+4)=sqrt104#

The modulus of #vecC# is

#∥vecC∥=∥〈-1,7,6〉∥=sqrt(1+49+36)=sqrt86#

Therefore,
#costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=62/(sqrt104*sqrt86)=0.66#

#theta=49#º