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Families of straight lines

  1. May 16, 2008 #1
    This is my second post on PF =)
    I want to ask what is the use of Families of straight lines?
    I am thinking of A Family of Straight Lines Passing Through the Intersection of Two Lines.
    We have the equation: L1+kL2=0 where L1=L2=0 and k is a variable, right?
    But is it said that L2 is not included in this family?
    So why are we using this equation, when it cannot fully represent all the lines with this common properties, so as to classify them into a family?
    Please, may you help. Thanks
  2. jcsd
  3. May 16, 2008 #2


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    "We have the equation: L1+kL2=0 where L1=L2=0 and k is a variable, right?"

    I cannot make sense out of that sentence. If "L1= L2= 0 and k is a variable" then the equation L1+ kL2= 0 just says "0= 0". It says nothing about any "family of straight lines".
  4. May 17, 2008 #3
    Maybe I wasn't making the question clear enough...

    Here's what I find in my textbook:

    So why don't we use the last equation instead?
  5. May 17, 2008 #4


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    Welcome to PF!

    Hi theow ! Welcome to PF! :smile:
    Yes … L1 is included, because L1 = L1 + kL2 with k= 0.

    But there is no k (unless you include infinity, which is not allowed) for which L2 = L1 + kL2, is there? :smile:
    We do … your textbook says:
    We use lL1 + mL2. :smile:
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