Question

What is the angle between `<5,4,3 >` and `< 1,-5,-7 >`?

Answer 1

The angle is `126`º

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=〈5,4,3〉.〈1,-5,-7〉=5-20-21=-36`

The modulus of `vecA`= `∥〈5,4,3〉∥=sqrt(25+16+9)=sqrt50`

The modulus of `vecB`= `∥〈1,-5,-7〉∥=sqrt(1+25+49)=sqrt75`

So,

`costheta=(vecA.vecB)/(∥vecA∥*∥vecB∥)=-36/(sqrt50*sqrt75)=-0.588`

`theta=126`º