Question

What is the angle between `<4 , 7 , -1 >` and `< -3 , 6 , 3 >`?

Answer 1

The angle is `=63.3^@`

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=〈4,7,-1〉.〈-3,6,3〉=-12+42-3=27`

The modulus of `vecA`= `∥〈4,7,-1〉∥=sqrt(16+49+1)=sqrt66`

The modulus of `vecB`= `∥〈-3,6,3〉∥=sqrt(9+36+9)=sqrt54`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=27/(sqrt66*sqrt54)=0.45`

`theta=63.3^@`