Vectors. Am I correct? (with working)

Question

Is my working correct? For some reason I don't think e looks correct. Any feedback is appreciated.

a) Vector (AC) → can be computed as the difference between the coordinates at point C and point A: (-5,5,-1).

b) Vector (AB) → can be computed as the difference between the coordinates at point B and point A: (1,1,1);

The length of Vector AB → = √ (1^2 + 1^2 + 1^2) = √3.

c) Vector BC → can be computed as the difference between the coordinates at point C and Point B: (-6,4,-2); The midpoint of this vector is (-3,2,-1).

d) Unit vector in the direction of vector (AB) →: 1/√3(i + j + k)

e) Vector AB → ° Vector AC → (Dot Product) = (1x-5) + (1x5) + (1x-1) = -5+5-1 = -1 = ||AB|| ||AC|| cos (θ)

-1 = (√3) (√51) cos (θ)

cos (θ) = -1 / √153

θ = arcos (-1 / √153) = 85.36 degrees

Answer 1

All the answers are correct except $c)$: the coordinates of the midpoint of $B$ and $C$ are the half of the sum of the coordinates of $B$ and $C$: $(-1,1,3)$.

Answer 2

Your answer to c) is midpoint of the vector BC translated in such a way that point B corresponds to the origin of the coordinate system and that is not the midpoint of the straight line between points B and C and that is what is being asked, so all is correct except c) as already was pointed out in an answer given before this one, this is just to tell you what did you calculate in your c).