Question

Question #89959

Answer 1

The angle is `=41`º

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=〈2,3,1〉.〈4,1,2〉=8+3+2=13`

The modulus of `vecA`= `∥〈2,3,1〉∥=sqrt(4+9+1)=sqrt14`

The modulus of `vecB`= `∥〈4,1,2〉∥=sqrt(16+1+4)=sqrt21`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=13/(sqrt14*sqrt21)=0.758`

`theta=41`º