Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

enter image description here

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

share|improve this question

2 Answers 2

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

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

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).

share|improve this answer
    
Thanks a bunch for the feedback. I knew I'd gone wrong somewhere. –  Laura Anderson Aug 20 '13 at 8:37
    
@Laura Anderson It is not a big mistake, also it is easy to go astray sometimes, you´re welcome. :) –  user90628 Aug 20 '13 at 8:40

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.