# If A = <36 ,1 ,5 >, B = <4 ,6 ,-1 > and C=A-B, what is the angle between A and C?

Feb 4, 2017

The angle is $= 0$º

#### Explanation:

Let's start by calculating

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

vecC=〈36,1,5〉-〈4,6,-1〉=〈32,-5,6〉

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=〈36,1,5〉.〈32,-5,6〉=1152-5+30=1177

The modulus of $\vec{A}$= ∥〈36,1,5〉∥=sqrt(1226+1+25)=sqrt1252

The modulus of $\vec{C}$= ∥〈32,-5,6〉∥=sqrt(1024+25+36)=sqrt1085

So,

costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=1177/(sqrt1252*sqrt1085)=1

$\theta = 0$º