Question

What is the angle between `<-4,0,1 >` and `<-6,-1,0>`?

Answer 1

The angle is `=16.9º`

Explanation:

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

`vecA.vecB=∥vecA∥*∥vecB∥costheta`

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

The dot product is

`vecA.vecB=〈-4,0,1〉.〈-6,-1,0〉=24+0+0=24`

The modulus of `vecA`= `∥〈-4,0,1〉∥=sqrt(16+0+1)=sqrt17`

The modulus of `vecB`= `∥〈-6,-1,0〉∥=sqrt(36+1)=sqrt37`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=24/(sqrt17*sqrt37)=0.96`

`theta=16.9`º