Question

If `A = <4 ,2 ,5 >`, `B = <6 ,2 ,8 >` and `C=A-B`, what is the angle between A and C?

Answer 1

2.82 radians`≈ 162^@`

Explanation:

To calculate the angle between 2 vectors `ula " and " ulc`
the following should be used.

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

here C= A - B = (4,2,5) - (6,2,8) = (-2,0,-3)

now `ula . ulc = (4,2,5) . (-2,0,-3)`

`=(4xx-2) + (2xx0) + (5xx-3)`

= -8 + 0 -15 = - 23

`|ula| = sqrt(4^2+2^2+5^2) = sqrt(16+4+25) = sqrt45`

and `|ulc| = sqrt((-2)^2+0+(-3)^2) = sqrt(4+0+9) = sqrt13`

`rArr theta = cos^-1(-23/(sqrt45 xx sqrt13)) ≈ 2.82 " radians"`