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Vector Problem

  1. Dec 15, 2009 #1
    1. The problem statement, all variables and given/known data
    The greek letters look like they're superscripted, they're not supposed to be.
    a, b, c are vectors

    given that
    [tex]\lambda[/tex]a + [tex]\mu[/tex] b + [tex]\nu[/tex]c=0

    show that the points [tex]\alpha[/tex]a, [tex]\beta[/tex]b and [tex]\gamma[/tex]c are collinear if

    [tex]\lambda[/tex]/[tex]\alpha[/tex] + [tex]\mu[/tex]/[tex]\beta[/tex] + [tex]\nu[/tex]/[tex]\gamma[/tex] = 0

    2. Relevant equations

    There are a lot of potentially relevant equations. Most important:
    lines are collinear if a = xb

    3. The attempt at a solution
    My attempt is really long so I won't post it here, I'll just outline my method.

    I found the line between [tex]\alpha[/tex]a and [tex]\beta[/tex]b and said it was equal to x times the line between [tex]\beta[/tex]b and [tex]\gamma[/tex]c.

    I also found a in terms of b and c from
    [tex]\lambda[/tex]a +[tex]\mu[/tex]b + [tex]\nu[/tex]c=0

    and subbed it into the former equation. However I got stuck because I had an x that I couldn't get rid of.
  2. jcsd
  3. Dec 16, 2009 #2


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    Science Advisor
    Homework Helper

    Hi thepopasmurf! :smile:
    Nooo … most important is the cross product equation, (p - q) x (q - r) = 0. :wink:
  4. Dec 16, 2009 #3
    Thank you, solved it. I forgot about that one
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