Question

What is the angle between `< 4 , 1 , -2 >` and `< -9 , -3 , 2 >`?

Answer 1

The angle is `=165.4^@`

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=〈4,1,-2〉.〈-9,-3,2〉=(4)*(-9)+(1)*(-3)+(-2)*(2)=-43`

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

The modulus of `vecB`= `∥〈-9,-3,2〉∥=sqrt(81+9+4)=sqrt94`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-43/(sqrt21*sqrt94)=-0.97`

`theta=arccos(-0.97)=165.4^@`