# If A = <2 ,3 ,6 >, B = <5 ,1 ,7 > and C=A-B, what is the angle between A and C?

Nov 20, 2016

The angle is $= 103.2$º

#### Explanation:

Let's start by calculating $\vec{C}$

vecC=vecA-vecB=〈2,3,6〉-〈5,1,7〉=〈-3,2,-1〉

The angle betwwen two vectors is given by the dot product.

vecA.vecC=∥vecA∥*∥vecC∥*costheta

Where $\theta$ is the angle between the 2 vectors.

The dot product is

vecA.vecC=〈2,3,6〉.〈-3,2,-1〉=-6+6-6=-6

The modulus of $\vec{A}$ is
∥vecA∥=∥〈2,3,6〉∥=sqrt(4+9+36)=sqrt49=7

The modulus of $\vec{C}$ is
∥vecC∥=∥〈-3,2,-1〉∥=sqrt(9+4+1)=sqrt14

Therefore,
$\cos \theta = - \frac{6}{7 \sqrt{14}} = - 0.23$

$\theta = 103.2$º