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Parametric equations and lines

  1. Sep 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine if any of the lines are parallel or identical
    L1 (x-8)/4 = (y+5)/-2 = (z+9)/3
    L2 (x+7)/2 = (y-4)/1 = (z+6)/5
    L3 (x+4)/-8 = (y-1)/4 = (z+18)/-6
    L4 (x-2)/-2 = (y+3)/1 = (z-4)/1.5

    2. Relevant equations
    L1 pt(8,-5,-9) V<4,-2,3>
    L2 pt(-7,4,-6) V<2,1,5>
    L3 pt(-4,1,-18) V<-8,4,-6>
    L4 pt(2,-3,4) V<-2,1,1.5>

    3. The attempt at a solution
    I know that if the vectors are scalar multiples, they are either parallel or identical. What I don't know, is after I find out that V(L3) = -2*V(L1). How do I determine if they are parallel or identical. I assume that since one vectors k value is 1.5, it is some multiple of another line, if not they wouldn't have given a 1.X. So L1 L3 L4 are parallel but how could I find if they were identical or not?
    Last edited: Sep 16, 2008
  2. jcsd
  3. Sep 17, 2008 #2
    After careful consideration, and pulling my head out of the book to think logically, I realized after I find the parallel lines, if a point I chose that satisfies one equation, also satisfies another line equation, they are identical, if its not on the line, it's still parallel, just not identical. That was 1.5 hours wasted on a brain fart!
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