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Ratios between vectors

  1. Apr 13, 2014 #1
    1. The problem statement, all variables and given/known data

    question attached

    2. Relevant equations



    3. The attempt at a solution
    i cant understand III
    i cant understand what he wants , if he wants the ratio , the ratio between AP and PB was 3/5
    which is not the same as OA and OB
    (λ=3/8)
     

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  2. jcsd
  3. Apr 13, 2014 #2

    Mark44

    Staff: Mentor

    Show us how you arrived at these values.
     
  4. Apr 13, 2014 #3
    Sure, the 3/8 ( i am sure it's correct ) was ii and it's a bit long to write it on the computer, but if it's important for you to know i can write it, as for iii.
    As for AP, was mentioned that AP=λAB , AB=OB-OA=(2i+2j-2k)
    AP= 3/8 * (2i+2j-2k) = ( 3/4 i + 3/4 j -3/4 k )
    PB = OB-OP= (3i+4j) - (7/4 i + 11/4 j - 5/4 k )= (5/4 i+ 5/4 j - 5/4 k )
    so ratio between them (if thats what he wants) is (5/4) / (3/4) =5/3
    there is no ratio between OA and OB , what does he mean by (:) anyway?
     
  5. Apr 13, 2014 #4

    Mark44

    Staff: Mentor

    There's no such thing as the ratio between two vectors, but you can calculate the ratio of their magnitudes or lengths.
    The ratio OA:OB means |OA|/|OB|.
     
  6. Apr 13, 2014 #5
    i tried to come with the ratio between the magnitudes , they were not equal , AP:PB gave 15/16 and OA:OB gave 3/5
     
  7. Apr 14, 2014 #6

    Mark44

    Staff: Mentor

    You have a mistake in what you have for |AP| or |PB|.
    When λ = 3/8,
    AP = (3/4)<1, 1, -1>
    and PB = (2 - 3/4)<1, 1, -1> = (5/4)<1, 1, -1>.
    It makes it much simpler to simplify the vectors as I have done, before you calculate the magnitudes.


    If you fix your mistake, you should be able to confirm that
    $$ \frac{|\vec{AP}|}{|\vec{PB}|} = \frac{|\vec{OA}|}{|\vec{OB}|}$$
     
  8. Apr 15, 2014 #7
    okay..thanks
     
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