The given points A, B, C are the vertices of a triangle. Determine the vectors `vec(AB),vec(BC)` and `vec(CA)` and the lengths of these vectors in the following case.
A(4,5,5), B(3,3,3), C(1,2,5)

Explanation

`vec(AB)` = `(3-4)hati + (3-5)hatj + (3-5)hatk = `-hati -2hatj-2hatk`
`vec(BC)` = `(1-3)hati + (2-3)hatj + (5-3)hatk` = `-2hati -hatj+2hatk`
`vec(AC)` = `(1-4)hati + (2-5)hatj + (5-5)hatk` = `-3hati - 3hatj`
vec(CA)` = `3hati+3hatj`
The length of `vec(AB)` = AB =`sqrt(1+4+4)` = 3
The length of `vec(BC)` = BC = `sqrt(4+1+4)` = 3
The length of `vec(CA)` = CA = `sqrt(9+9)` = `3sqrt2`