Question

What is the angle between `<-9 , 2 , 2 >` and `< 5 , 8 , 3 >`?

Answer 1

The angle is `=103.6^@` anticlockwise from the x-axis

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=〈-9,2,2〉.〈5,8,3〉=-45+16+6=-22`

The modulus of `vecA`= `∥〈-9,2,2〉∥=sqrt(81+4+4)=sqrt89`

The modulus of `vecC`= `∥〈5,8,3〉∥=sqrt(25+64+9)=sqrt98`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-22/(sqrt89*sqrt98)=-0.24`

`theta=arccos(-0.24)=103.6^@` anticlockwise from the x-axis