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Homework Help: Vector problems

  1. Sep 9, 2010 #1
    1.Determine if it is true that for any vectors a, b, c such that
    a is not equal to 0 and a‧b = a‧ c, then b = c.



    i tried to let a‧b-a‧c=0
    then a‧(b-c)=0
    but i found it's not meaningful
    so how can i solve it =[
    thz
     
  2. jcsd
  3. Sep 9, 2010 #2

    radou

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    Try to think of an example where it's not true.
     
  4. Sep 9, 2010 #3
    the method i have tried is really useless?
     
  5. Sep 9, 2010 #4

    radou

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    It's not useless, it just doesn't tell you anything.

    You can solve this by finding a counterexample.
     
  6. Sep 9, 2010 #5
    assume b is not equal to c
    l.h.s=a‧b
    =...
    should i express the dot product?
     
  7. Sep 9, 2010 #6

    radou

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    let a = (1, 0, 0), b = (1, 0, 1), c = (1, 2, 1).

    What does a.(b - c) equal?
     
  8. Sep 9, 2010 #7
    zero =[
    btw,when we want some example for conradiction,we should use some real number to think about it first?
     
  9. Sep 9, 2010 #8

    radou

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    It doesn't matter what you use.

    If you're not talking about a specific set of vectors and a specific dot product, and if you assume that, for any non-zero a, and any b, c, the implication a.(b - c) = 0 ==> b = c holds (which is equivalent to a.b = a.c ==> b = c) then it doesn't matter which vector space and dot product you chose to construct your counterexample.

    So, we found an example where a.(b - c) = 0, when b doesn't equal c.
     
  10. Sep 9, 2010 #9
    a.(b - c) = 0, when b doesn't equal c
    this i'd thought once,but dunno how to express
    anyway thank you very much :p
     
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