Question

What is the angle between `<7,-3,1>` and `< -1,3,2 >`?

Answer 1

Angl between above vctors `119.2^0`

Explanation:

Let `vec u =[7, -3, 1] ; vec v=[-1,3,2]` and `theta` be the angle between them. We know `cos theta= (vec u. vec v)/(||vec u||.||vec v||)` Now `vec u . vec v= (7 * -1) + (-3*3) + (1*2) = -14` ; `|| vecu || = sqrt(7^2 +(-3)^2 +1^2) =sqrt 59` and `|| vec v || = sqrt((-1)^2 +(3)^2 +2^2) =sqrt 14` `:. cos theta= -14/(sqrt59 * sqrt 14) = -.487 or theta = cos^-1 (-.487)=119.2^0`[Ans]