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Abstract geometry I think

  1. Dec 28, 2011 #1
    1. The problem statement, all variables and given/known data

    (E) is a group of points M from a level/plane

    [tex]MA^{2}-MB^{2}=-4[/tex] And I is the center of [AB]

    2. Relevant equations

    show that IM*AB=-2 ( IM and AB have arrows on top)

    3. The attempt at a solution

    Well i split [tex]MA^{2}-MB^{2}=(MA-MB)(MA+MB)[/tex]

    then i got : [tex]MA^{2}-MB^{2}=BA*(MA+MB)[/tex]

    and i don't know where to go on from there any help?
     
    Last edited: Dec 28, 2011
  2. jcsd
  3. Dec 28, 2011 #2

    Mark44

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    This doesn't make any sense to me.

    What is A? What is B? Is AB the line segment from point A to point B?
     
  4. Dec 28, 2011 #3
    My fault AB is a line segment and I is the center of it.
     
  5. Dec 28, 2011 #4

    SammyS

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    I think this is impossible! [itex]MA^{2}+MB^{2}=-4[/itex]

    Do you mean? [itex]MA^{2}-MB^{2}=-4[/itex]
     
  6. Dec 28, 2011 #5
    Yea sorry my fault that was a typo its MA^2-MB^2=-4
     
  7. Dec 28, 2011 #6
    Any ideas?
     
  8. Dec 28, 2011 #7

    Mark44

    Staff: Mentor

    What does this mean?
    Does * represent the dot product?
     
  9. Dec 28, 2011 #8
    Yes.
     
  10. Dec 28, 2011 #9

    SammyS

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    Since "IM and AB have arrows on top", and "AB is a line segment", I take it that these are all vectors and, for example, [itex]\vec{MB}[/itex] is a vector from point M to point B.

    If that's the case, then notice that [itex]\vec{MA}=\vec{MI}+\vec{IA}\,.[/itex] Do similar for [itex]\vec{MB}[/itex]

    Notice that[itex]\vec{IB}=-\vec{IA}\,.[/itex]

    Now look at [itex]\vec{MA}+\vec{MB}[/itex] again.
     
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