Question

If `A = <3 ,8 ,-1 >`, `B = <4 ,-7 ,-1 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`0.44 " radians " (25.21^@)`

Explanation:

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

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

where `theta " is the angle between " ula " and " ulc`

now C = A - B = (3,8,-1) - (4,-7,-1) = (-1,15,0)

`ula . ulc = (3,8,-1) . (-1,15,0)`

`= (3xx-1)+(8xx15)+(-1xx0) = -3 + 120 = 117`

`|ula| = sqrt(3^2+8^2+(-1)^2) = sqrt(9+64+1) = sqrt74`

and `|ulc| = sqrt((-1)^2+15^2+0) = sqrt(1+225) = sqrt226`

`rArrtheta = cos^-1(117/(sqrt74xxsqrt226)) ≈ 0.44" radians "`