Question

What is the angle between `<7,-3,1 >` and `< -2,8,-5 >`?

Answer 1

`2.19" radians " (125.5^@)`

Explanation:

To calculate the angle between 2 vectors `ula " and " ulb " use"`

`costheta = (ula . ulb)/(|ula||ulb|)`

let `ula = (7,-3,1) " and " ulb = (-2,8,-5)`

(1) calculate the`color(blue)" the dot product "ula . ulb "`

`ula . ulb = (7,-3,1) . (-2,8,-5)`

`= (7xx-2) + (-3xx8) + (1xx-5) = -14-24-5 = -43`

(2) calculate the`color(blue) " magnitudes of " ula , ulb`

`|ula| = sqrt(7^2+(-3)^2+1^2) =sqrt(49+9+1) = sqrt59`

`|ulb| = sqrt((-2)^2+8^2+(-5)^2)=sqrt(4+64+25) =sqrt93`

`rArr theta = cos^-1((-43)/(sqrt59xxsqrt93)) = 2.19 " radians "`