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Expressing A Vector Given Another Vectors

  1. Jul 6, 2012 #1
    1. The problem statement, all variables and given/known data
    ABCD is a square (AB = AD = BC = CD). The point P and Q are located in the middle of BC and CD. If AP and AD is expressed by the name vector a and b, then AQ = ...
    A) (1/2)a + (3/4)b
    B) (1/3)a + (2/3)b
    C) (3/4)a + (1/2)b
    D) (2/3)a + (1/3)b
    E) (2/3)a + (3/4)b


    2. Relevant equations
    Vector addition law (still confused)


    3. The attempt at a solution
    This problem comes in a competition about 4 months ago. I just chose the answer A (random guessing) and thank God the answer is A. But how do we find it?
     
  2. jcsd
  3. Jul 6, 2012 #2

    tiny-tim

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    welcome to pf!

    hi wiraimperia! welcome to pf! :smile:

    for some reason, AD is called "b" :rolleyes:

    so let's call AB "d" :biggrin:

    then express everything in terms of b and d …

    what do you get? :smile:
     
  4. Jul 6, 2012 #3

    ehild

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    A picture always helps.

    ehild
     

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  5. Jul 6, 2012 #4

    tiny-tim

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    :tongue2:
     
  6. Jul 6, 2012 #5
    Re: welcome to pf!

    We refer to the multiple choice answers... Not a made-up answer... And I'm still confused why it is (1/2)a + (3/4)b :confused:
     
  7. Jul 6, 2012 #6

    ehild

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    Pretend that it is a "made-up" problem and find the vector AQ in terms of a and b. Follow tiny-tim's hint.

    ehild
     
  8. Jul 6, 2012 #7
    Remember a vector can be represented by a segment of a line
    You can put anywhere the line/vector with the same direction/parallel.
     
  9. Jul 6, 2012 #8
    Just draw two lines through Q, one parallel to b and the other parallel to a. These lines will cut b and a to the appropriate lengths and these lenghts can be determined by using the similarity triangles in the case of a and the 30-60 triangle in the case of b.
     
    Last edited: Jul 6, 2012
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