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

Nov 2, 2016

The angle is =66.1º

#### Explanation:

The angle between 2 vectors is given by the dot product.
If we have two vectors $\vec{A}$ and $\vec{C}$, then the angle $\theta$
is given by costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)
vecC=〈2,-7,5〉-〈5,-7,-1〉=〈-3,0,6〉
The dot product 〈2,-7,5〉.〈-3,0,6〉=-6+0+30=24
The modulus of ∥vecA∥=sqrt(4+49+25)=sqrt78
The modulus of ∥vecC∥=sqrt(9+0+36)=sqrt45

So $\cos \theta = \frac{24}{\left(\sqrt{78}\right) \left(\sqrt{45}\right)} = 0.41$
theta= arccos(0.41)=66.1º