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United States Multivariable Calculus - Vectors in Three Dimensions

  1. Dec 28, 2011 #1
    1. The problem statement, all variables and given/known data

    See attachment

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure how to determine which points are co linear or which point lies in between the two. My book doesn't discuss how to do this at all.

    PQ→ = <1,-1,2>, PR→ = <3,-3,6>
    I believe I found these correctly but I'm not sure what to do from here. Thanks for any help anyone can provide.

    Attached Files:

  2. jcsd
  3. Dec 28, 2011 #2


    Staff: Mentor

    PR is a multiple of PQ. Doesn't that tell you something?
  4. Dec 28, 2011 #3
    there parallel to each other but i don't know how that helps me answer the question
  5. Dec 28, 2011 #4
    Imagine a similar setup in two dimensions. Suppose you are given three points, P, Q, and R in the x-y plane. Now suppose (as is the case in the original problem) that PQ is a multiple of PR. Try to make a graph of this scenario to convince yourself that the three points are colinear. Will this still be the case when we move up to three dimensions?
  6. Dec 28, 2011 #5
    hm i didn't think of it like that interesting
    ok so they are indeed co linear then
    can i find the magnitude of pq and pr and then just compare which one is smaller to determine if q lies in between p and r or if r lies between p and q?
  7. Dec 28, 2011 #6
    Yes. You will compare distances to determine which point lies between the other two. Be sure to use the two dimensional analogy again if you get stuck (and keep it in mind for future problems :smile:).
  8. Dec 28, 2011 #7
    thanks for your help
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