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Homework Help: Simple vector question

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Given A(1,7) and B(8,3). C lies on OB where O is the origin. If vector OA + BA + CA is perpendicular to vector OB, find the coordinates of C.

    2. Relevant equations

    3. The attempt at a solution

    The answer i get is C=(112/73 , 42/73) but the answer given is (-71/2 , 195/7). What answer do you get? :smile:
  2. jcsd
  3. Oct 3, 2011 #2


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    Staff: Mentor

    Have you messed up in writing out this question?
  4. Oct 3, 2011 #3
    I agree, I think you may have written something wrong there.

    The easiest way is using the dot product, as (OA+OB+OC) . (OB) = 0, then you'd get two equations, one for each C co-ordinate, that'd be easy to solve.

    However I don't get the answer you say you were given.
  5. Oct 4, 2011 #4
    Why (OA+OB+OC) . (OB) = 0?

    What's wrong with the question? Here is how i do.. probably someone can check it out for me...

    C lies on OB, so C = k(8,3)

    BA = OA-OB = (-7,4)

    CA= OA-OC = (1-8k, 7-3k)

    OA + BA + CA = (-5-8k, 18-3k)

    OA + BA + CA is perpendicular to vector OB, so

    OA + BA + CA . OB = 0

    (-5-8k, 18-3k) . (8,3)=0

    -8(5+8k) + 3(18-3k) = 0

    k= 14/73

    So C = k(8,3) = 14/73 . (8,3)

    Which step have i go wrong?
  6. Oct 4, 2011 #5


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    Staff: Mentor

    The question is okay. I was expecting a more common question, a little simpler. :smile:
  7. Oct 4, 2011 #6


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    Staff: Mentor

    The book's answer can't be correct. OB is in the first quadrant, so no point on it has an x-coordinate with a negative value. I reckon you could easily plot this exercise on graph paper, and determine the point C with sufficient accuracy to confirm (or not) your answer.

    I looked at this, and found C as (232/73, 87/73) , just fractionally more than double what you calculated. I haven't checked my working though.
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