Question

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

Answer 1

See below

Explanation:

We will be using:
`costheta= (u*v)/(||u||*||v||)`

Let:
`u` be the `<1,5,7 >`
`v` be the `< 4, 7, 3 >`

The vectors are defined in their component form, therefore, their x,y, and z value changes are described from (0,0,0), so for the distance of each vector:

`||u||= sqrt(1^2+5^2+7^2)= 5sqrt3`

`||v||= sqrt(4^2+7^2+3^2)= sqrt74`

The dot product `u` and `v` is:
`u*v=1*4+5*7+7*3=60`

So for the angle between them:
`theta= arccos((60)/(5sqrt3*sqrt74))approx 36.352 ^@`