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Vector relationship? |A+B| = |A-B|

  1. Sep 7, 2011 #1
    I've been spending far too much time on this problem and I know I'm over thinking it. Here it is:

    If |A+B| = |A-B|

    What is the most general relationship between the two vectors?

    -Now I know this is just saying they have equal magnitude regardless of direction, but I'm not quite sure what it's asking for. What kind of general relationship am I supposed to write out? Any help would be greatly appreciated. Thanks!
     
  2. jcsd
  3. Sep 7, 2011 #2

    micromass

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    Try to calculate this norms with the inner product:

    [tex]|A|^2=<A,A>[/tex]
     
  4. Sep 7, 2011 #3
    I'm still not seeing how to relate vector A and B using this.. =/
     
  5. Sep 7, 2011 #4

    micromass

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    What did you get when you wrote it out:

    [tex]|A+B|^2=<A+B,A+B>=...[/tex]

    [tex]|A-B|^2=...[/tex]

    ???
     
  6. Sep 7, 2011 #5
    [itex]<A+B,A+B>=<A-B,A-B>[/itex]
    By properties of the dot product..
    [itex]<A,A>+2<B,A>+<B,B>=<A,A>-2<B,A>+<B,B>[/itex]

    Get everything to one side and deduce from that.
     
  7. Sep 7, 2011 #6
    We haven't learned this notation yet unfortunately. Is this the only possible approach?
     
  8. Sep 7, 2011 #7

    micromass

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    What is yor notation for the dot product then??
     
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