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

Nov 12, 2016

The angle is $49.6$º

#### Explanation:

Let's start by calculating vecC=vecA-vecB=〈5,4,3〉-〈2,-7,5〉

vecC=〈3,11,-2〉

To calculate the angle, we use the dot productt definition,

vecA.vecC=∥〈5,4,3〉∥*∥〈3,11,-2〉∥*costheta
where $\theta$ is the angle between the 2 vectors

vecA.vecC=〈5,4,3〉.〈3,11,-2〉=15+44-6=53

Modulus of vecA=∥〈5,4,3〉∥=sqrt(25+16+9)=sqrt50

Modulus of vecC=∥〈3,11,-2〉∥=sqrt(9+121+4)=sqrt134

:. cos theta=53/(sqrt50*sqrt134=0.65

$\theta = 49.6$º