# If A = <7 ,-5 ,-2 >, B = <4 ,-8 ,-3 > and C=A-B, what is the angle between A and C?

##### 1 Answer
Jan 10, 2017

The angle is $= 84.04$º

#### Explanation:

Let's start by calculating

$\vec{C} = \vec{A} - \vec{B}$

vecC=〈7,-5,-2〉-〈4,-8,-3〉=〈3,3,1〉

The angle between $\vec{A}$ and $\vec{C}$ is given by the dot product definition.

vecA.vecC=∥vecA∥*∥vecC∥costheta

Where $\theta$ is the angle between $\vec{A}$ and $\vec{C}$

The dot product is

vecA.vecC=〈7,-5,-2〉.〈3,3,1〉=21-15-2=4

The modulus of $\vec{A}$= ∥〈7,-5,-2〉∥=sqrt(49+25+4)=sqrt78

The modulus of $\vec{C}$= ∥〈3,3,1〉∥=sqrt(9+9+1)=sqrt19

So,

costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=4/(sqrt78*sqrt19)=0.104

$\theta = 84.04$º