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Vectors (Magnitude)

  1. Mar 21, 2011 #1


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    1. The problem statement, all variables and given/known data
    "The point C lies between A and B and is 5 units from A.

    OA = 2i + 3j
    OB = -4i - 5j

    Find OC."

    2. Relevant equations
    Pythagoras' Theorem

    3. The attempt at a solution
    This is not exactly a homework question since this is independent study, but I was wondering why I couldn't get the same answer as my textbook unless my textbook is wrong - but if it isn't, then that means I haven't grasped this topic yet.

    First find the vector AB;

    AB = OB - OA
    AB = -4i - 5j - 2i - 3j = -6i - 8j

    The magnitude of AB is therefore 10, by Pythagoras' Theorem.

    Since C is 5 units from A and lies between A and B;

    AC = (AB)/2

    AC = 0.5(-6i - 8j) = -3i - 4j

    To find OC, we simply substitute values into the equation OA + AC = OC;

    OA + AC = OC
    2i + 3j - 3i - 4j = -i - j = OC

    So OC should be -i - j, but I don't see the error I have made... my textbook says it should be 0.8i + 1.4j. This problem has been bugging me because I thought I understood this, perhaps there is something deeper I haven't noticed/considered?

  2. jcsd
  3. Mar 21, 2011 #2


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    Hello FeDeX_LaTeX! :smile:

    Your method looks correct to me. :confused:

    Perhaps the question should say 2 units instead of 5 ?
  4. Mar 21, 2011 #3


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    Thank you for the quick reply!

    I did the problem again assuming it was 2 units from A, not 5, and I did indeed get the textbook's answer. But the problem does say 5 units. I suppose it is just a typo.

    Thanks! Now just one more topic and I've finished this chapter.
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