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Given Vector

  1. Apr 1, 2005 #1
    help this:
    If a is a given vector and a.b=a.c can we conclude that a=b?
     
  2. jcsd
  3. Apr 1, 2005 #2

    arildno

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    Dearly Missed

    Please read your exercise again.
    I am quite certain you have written it down wrongly..
     
  4. Apr 1, 2005 #3

    dextercioby

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    I'm sure it asks about

    [tex] \vec{a}\cdot\vec{b}=\vec{a}\cdot\vec{c}\Rightarrow \vec{b} \ ? \ \vec{c} [/tex]

    Daniel.
     
  5. Apr 1, 2005 #4
    in which case, here's a hint: Let [itex] a = (1, 1)[/itex]. Can you think of two different vectors that when dotted with [itex]a[/itex] give you [itex]1[/itex]?
     
  6. Apr 1, 2005 #5
    I have written it correct, If a is a given vector and a.b=a.c can we conclude that a=b?
     
  7. Apr 1, 2005 #6

    chroot

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    kidia,

    In that case, it's a "trick question." You have no idea what c is, so you cannot conclude anything.

    - Warren
     
  8. Apr 1, 2005 #7
    ...

    well, for any [itex]a, b[/itex] you have [itex] a \cdot b = a \cdot b[/itex], and it's certainly possible to have [itex]a \neq b[/itex], so uhh... no.
     
  9. Apr 1, 2005 #8

    dextercioby

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    BTW,the solution to the problem i proposed is

    [tex] \vec{b}=\vec{c}+\vec{a}\times\vec{k} [/tex],where [itex] \vec{k} [/itex] is arbitrary...

    Daniel.
     
  10. Apr 1, 2005 #9

    matt grime

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    in 3 dimensions :wink: (i hate smilies but thought there shuold be some tongue in cheek indicator)
     
    Last edited: Apr 1, 2005
  11. Apr 1, 2005 #10
    May be the answer is no we cannot conclude that a=b but I am not sure
     
  12. Apr 1, 2005 #11

    dextercioby

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    On what basis could you draw a correct conclusion,given the problem in its form...?

    Daniel.
     
  13. Apr 4, 2005 #12
    The answer is no.

    Let a=x-hat, b=y-hat, c=z-hat.

    a.b = a.c = 0. Note that the 0 does not trivialize the result. You can
    find infinite non-zero vectors with non-zero dot products that could
    satisfy the relation.
     
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