Question

What is the angle between `<-5,7,6 >` and `<0,-4,8>`?

Answer 1

The angle is `=77.7`º

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 the 2 vectors

Here,

`veca=〈-5,7,6〉`

`vecb=〈0,-4,8〉`

The dot product is `veca.vecb=〈-5,7,6〉.〈0,-4,8〉`

`=0-28+48=20`

The modulus of `veca=∥〈-5,7,6〉∥=sqrt(25+49+36)=sqrt110`

The modulus of `vecb=∥〈0,-4,8〉∥=sqrt(0+16+64)=sqrt80`

`costheta=(veca.vecb)/(∥veca∥*∥vecb∥)=20/(sqrt110*sqrt80)`

`costheta=0.21`

`theta=77.7`º