Question

What is the angle between `<5,7,1>` and `<5,1,7>`?

Answer 1

The angle is `58.7`º

Explanation:

The angle between `vecA` and `vecB` is given by the dot product definition.

`vecA.vecC=∥vecA∥*∥vecB∥costheta`

Where `theta` is the angle between `vecA` and `vecB`

The dot product is

`vecA.vecB=〈5,7,1〉.〈5,1,7〉=25+7+7=39`

The modulus of `vecA`= `∥〈5,7,1〉∥=sqrt(25+49+1)=sqrt75`

The modulus of `vecC`= `∥〈5,1,7〉∥=sqrt(15+1+49)=sqrt75`

So,

`costheta=(vecA.vecC)/(∥vecA∥*∥vecC∥)=39/(sqrt75*sqrt75)=39/75=0.52`

`theta=58.7`º