Question

What is the angle between `<2,-3,-1 >` and `< -8,3,-5>`?

Answer 1

`cos theta=(<2,-3,-1>*<-8,3,-5>)/((sqrt(2^2+(-3^2)+(-1)^2)) (sqrt((-8)^ 2+3^2+(-5)^2))`
=`(2(-8)+(-3)(3)+(-1)(-5))/((sqrt(14)sqrt(98))`
=`-20/sqrt1372`
`theta=cos^-1(-20/sqrt(1372))=122.68^@`

Explanation:

To find theta take the inverse cosine of the dot product of the given vectors divided by the product of the magnitude of each of the vectors.