Question

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

Answer 1

`costheta=(<5,2,-1>*<1,-3,1>)/(sqrt(5^2+2^2+(-1)^2)sqrt(1^2+(-3)^2+1^2))->costheta = (5(1)+2(-3)+(-1)1)/(sqrt(30) sqrt(11))->theta=cos^-1(-2/sqrt330)`
`theta=96.32^@`

Explanation:

To find the angle between the vectors use the formula `cos theta=(a*b)/(|a||b|`. Note that a and b are vectors and `a*b`is the dot product of the vectors