1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    NascentOxygen

    User Avatar

    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

    NascentOxygen

    User Avatar

    Staff: Mentor

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

    NascentOxygen

    User Avatar

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Simple vector question
  1. Simple vector question (Replies: 6)

  2. Simple Vector Question (Replies: 1)

Loading...