Question

What is the angle between `<-3,2,6 >` and `<5,0,-5>`?

Answer 1

2.71 radians ≈ `155.4^@`

Explanation:

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

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

let `ula = (-3,2,6) " and " ulb = (5,0,-5)`

hence `ula . ulb = (-3,2,6) . (5,0,-5)`

`= (-3xx5) + (2xx0) + (6xx-5)`

= -15 + 0 - 30 = - 45

`|ula| = sqrt((-3)^2+2^2+6^2) = sqrt(9+4+36) = sqrt49 = 7`

`|ulb| = sqrt(5^2+0+(-5)^2) = sqrt(25+0+25) = sqrt50`

`rArrtheta= cos^-1((-45)/(7xxsqrt50))= 2.71" radians"`