Question

What is the angle between `<9,-5,1 >` and `< -7,4,2 >`?

Answer 1

The angle is `=160.5^@`

Explanation:

The angle between `2` vectors `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=〈9,-5,1〉.〈-7,4,2〉=-63-20+2=-81`

The modulus of `vecA`= `∥〈9,-5,1〉∥=sqrt(81+25+1)=sqrt107`

The modulus of `vecB`= `∥〈-7,4,2〉∥=sqrt(49+16+4)=sqrt69`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-81/(sqrt107*sqrt69)=-0.943`

`theta=arccos(-0.943)=160.5^@`