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Vector equation of a line

  1. May 21, 2006 #1
    Points A, B and C lie on the line r = 2i + 3j + λ(i + 4j) and have position vectors given by λ=-1, λ=1 and λ=2 respectively.
    Find a) AB
    b) AB:BC
    The answer for part a is the square root of 17 (in exact form) however I keep getting the suare root of 20.
    Here is what I am doing:
    OB = 3i – j and OC = 5i – 5j
    BC= BO + OC
    BC= -(3i – j) + (5i – 5j)
    BC= 2i – 4j
    Therefore the magnitude of BC = square root of 20
    As for part b, I’m not sure what it’s asking me to do
    Last edited: May 21, 2006
  2. jcsd
  3. May 21, 2006 #2


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    Homework Helper

    I don't get it. The first part is asking for the magnitude of AB, yet you seem to be working out the magnitude of BC?:confused:

    In any case, your position vectors for both OB and OC are wrong. How did you do that? All you have to do is substitute the given values of λ into the equation to get the position vectors.

    Maybe I think it'd be better if you showed full working on how you get OA, OB and OC, because the first part is simple algebra.

    Part b) AB:BC is simply asking you to find the ratio between the lengths of the two line segments AB and BC. All you have to do is find |AB|, |BC| then take the ratio (I get two).
  4. May 21, 2006 #3
    sorry, it was meant to say the magnitude of BC, not AB. I have solved this now, so theres no need to worry bout it. As for part b), thanks for clearing that piont up, i should be able to work from here, otherwise i will re-post asking fro help
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