# Vectors. Am I correct? (with working)

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

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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 $C$: $(-1,1,3)$.

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Thank you @Sami! –  Laura Anderson Aug 20 '13 at 8:28
You're welcome. –  Sami Ben Romdhane Aug 20 '13 at 8:29