Question

If `A = <6 ,4 ,-7 >`, `B = <3 ,5 ,0 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`≈ 0.616" radians " (35.3^@)`

Explanation:

To calculate the angle between 2 vectors `ula" and " ulc`

use: `costheta = (ula . ulc)/(|a||c|)`

where `theta" is the angle between the vectors "`

now C = A - B = (6,4,-7)-(3,5,0) = (3,-1,-7)

so `ula . ulc =(6,4,-7) . (3,-1,-7)`

`= (6xx3)+(4xx-1)+(-7xx-7) = 18-4+49 = 63`

`|ula| = sqrt(6^2+4^2+(-7)^2) = sqrt(36+16+49)=sqrt101`

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

`rArr theta = cos^-1(63/(sqrt101xxsqrt59)) ≈ 0.616" radians "`