Question

What is the angle between `<-3 , -5 ,1 >` and `< -4, 7 ,-2 >`?

Answer 1

2.1 radians ≈ `120^@`

Explanation:

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

`costheta =( ula . ulb)/(|ula| |ulb|)`
where `theta " is the angle between the vectors"`

here let `ula =(-3 , -5 , 1 ) " and " ulb = (-4 ,7 , -2)`

hence `ula . ulb = (-3,-5,1) . (-4,7,-2)`

=(`-3xx-4) + (-5xx7) + (1xx-2)`

= 12-35-2 = -25

`|ula| = sqrt((-3^2)+(-5)^2+1^2) = sqrt(9+25+1) = sqrt35`

and`|ulb| = sqrt((-4)^2+7^2+(-2)^2) = sqrt(16+49+4) = sqrt69`

`rArr cos^-1((-25)/(sqrt35 xx sqrt69)) ≈ 2.1 " radians"`