Question

What is the angle between `<1 , -5 ,1 >` and `< -4, 9 , 4 >`?

Answer 1

The angle is `144.6 º`

Explanation:

let `veca=〈1,-5,1〉`

and `vecb=〈-4,9,4〉`

let `theta=(veca,vecb)` be the angle between the vectors

then by the definition of the dot product

`veca.vecb=∥veca∥∥vecb∥cos(veca,vecb)`
so `costheta=(veca.vecb)/(∥veca∥∥vecb∥)`
`veca.vecb=-4-45+4=-45`
`∥veca∥=sqrt(1+25+1)=sqrt27`
`∥vecb∥=sqrt(16+81+16)=sqrt113`

so `costheta=-45/(sqrt27 sqrt113)`

`theta=144.6º`