Question

What is the angle between `<5,8,2 >` and `< 2,1,4 >`?

Answer 1

The angle is `=54.0^@`

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=〈5,8,2〉.〈2,1,4〉=10+8+8=26`

The modulus of `vecA`= `∥〈5,8,2〉∥=sqrt(25+64+4)=sqrt93`

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

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=26/(sqrt93*sqrt21)=0.588`

`theta=arccos(0.588)=54.0^@`