Question

What is the angle between `<6 , 5 , 7 >` and `< 3 , 3 , 2 >`?

Answer 1

The angle is `=17.2`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=〈6,5,7〉.〈3,3,2〉=18+15+14=47`

The modulus of `vecA`= `∥〈6,5,7〉∥=sqrt(36+25+49)=sqrt110`

The modulus of `vecB`= `∥〈3,3,2〉∥=sqrt(9+9+4)=sqrt22`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=47/(sqrt110*sqrt22)=0.96`

`theta=17.2`º