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B About position vector

  1. Jul 30, 2016 #1
    While proving the Midpoints of the Sides of a Quadrilateral Form a Parallelogram , I got bogged down with position vectors.

    parallel.png
    Let a,b,c and d be the position vectors of A,B,C and D. But where is the origin? Aren't we supposed to locate position of origin?
     
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  3. Jul 30, 2016 #2

    PeroK

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    You can put the origin wherever you like. I might put it at point ##A##.
     
  4. Jul 30, 2016 #3
    If we take origin at A, position vector of A that is given to be a will be 0,0 . Right?
     
  5. Jul 30, 2016 #4

    cnh1995

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    As PeroK said, you can put the origin at any point as per your convenience.
    This problem can be solved using simple properties of triangle.
     
  6. Jul 30, 2016 #5

    PeroK

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    I'd say the position vector of ##A## in that case is ##\vec{0}##. This may simplify the problem.
     
  7. Jul 30, 2016 #6
    I want to use the following formula for position vector of mid point
    Su58k03_m27.gif
    For that I need origin other than point A.
     
  8. Jul 30, 2016 #7

    PeroK

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    That's the right formula, but it's even simpler with ##\vec{OA} = \vec{0}##.
     
  9. Jul 30, 2016 #8
    If we take ##\vec{OA}## = ##\vec{0}##
    The formula will be reduced to
    ##\vec{OM}## = ##\frac{OB}{2}##
    (I meant position vector of OB , I don't know how to get vector sign on top of OB)
     
  10. Jul 30, 2016 #9

    PeroK

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    Okay, that gives you the position vector of point ##P##.

    Have you thought yet about what you need to do to show that ##PQRS## is a parallelogram?
     
  11. Jul 30, 2016 #10
    In the book it's given
    PQ= position vector of Q - position vector of P
    How so? Is there any particular standard formula for this that I am missing?
     
  12. Jul 30, 2016 #11

    PeroK

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    It's not a formula. But, what defines a parallelogram?
     
  13. Jul 30, 2016 #12
    A Parallelogram has opposite sides parallel and equal in length.
     
  14. Jul 30, 2016 #13

    PeroK

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    Good. Think a bit more about what you need to do to show this.

    You can get from the origin to point ##Q## in two ways:

    ##\vec{OQ}##

    Or:

    ##\vec{OP} + \vec{PQ}##

    Therefore:

    ##\vec{OQ} = \vec{OP} + \vec{PQ}##
     
  15. Jul 30, 2016 #14
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