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Math Help - Equations of a line in three space.

  1. #1
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    Equations of a line in three space.

    The question: A line q is defined be the vector equation [x,y,z]=[4,-3,2] +t[1,8,-3]. Answer the following without technology.

    b) determine if line q intersects line r, defined by [x,y,z]=[2,-19,9]+s[4,-5,-9].

    I'm not sure how I would do this. I tried setting the parametric equations equal to each other and then solving for t and then subbing into one the original but I was getting a crazy answer. I have no idea how would i do this in 3-space. Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by darksoulzero View Post
    The question: A line q is defined be the vector equation [x,y,z]=[4,-3,2] +t[1,8,-3]. Answer the following without technology.
    b) determine if line q intersects line r, defined by [x,y,z]=[2,-19,9]+s[4,-5,-9].
    Solve this system \begin{gathered}<br />
  ~4 + t = 2 + 4s \hfill \\<br />
   - 3 + 8t = 19 - 5s \hfill \\ <br />
\end{gathered} if the solution also solves 2-3t=9-9s then they intersect.
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  3. #3
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    Thanks for the superfast reply. I appreciate your help, but I found out how do it when I googled it.
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    Quote Originally Posted by darksoulzero View Post
    Thanks for the superfast reply. I appreciate your help, but I found out how do it when I googled it.
    Can you googled it on a test?
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  5. #5
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    Actually, I found another site similar to this one and it had an example explaining the solution. Also, this is just extra practice and I wanted to try and get the answer on my own so I used google.
    Last edited by darksoulzero; March 26th 2011 at 05:22 PM.
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