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Math Help - Question on skew lines

  1. #1
    s3a
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    Question on skew lines

    The question is attached (#1, parts a and b). I have no idea how to do part b and as for part a. I don't remember what I did but when I try to think about the problem: I see that to find that the lines do not intersect I need to find that there is an inconsistence between the s[7,-1,-2] and t[1,1,2] slopes. (Is that what they're called?) Also, to find that they're not parallel I need some matrix to have only nonzero rows but I am confused as to which matrix I look at for the parallel one. Is it the same as the one where I looked for the inconsistence?

    If I'm unclear, please tell me.

    Any help would be GREATLY appreciated!
    Thanks in advance!
    Attached Thumbnails Attached Thumbnails Question on skew lines-temp_q.jpg  
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  2. #2
    MHF Contributor

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    If you really want help then you will type out the question in a readable format.
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  3. #3
    s3a
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    The question is already typed. (Could you rephrase your question please?)
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  4. #4
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    Quote Originally Posted by s3a View Post
    The question is already typed. (Could you rephrase your question please?)
    Well good luck with that non responsive reply.
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  5. #5
    s3a
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    I still don't get the problem, are you not able to see the image or something? I retyped it though like you asked:

    "Consider the lines l1: [-5,4,3] + s[7,-1,-2] and l2: [4,-1,8] + t[1,1,2].
    (a) Show that l1 and l2 are skew lines.
    (b) What is the distance between l1 and l2?"
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  6. #6
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    Given two skew lines: \ell _1 :P + tD\;\& \,\ell _2 :Q + tE
    then the distance between them is
    d\left( {\ell _1 ,\ell _2 } \right) = \left[ {\dfrac{{\left| {\overrightarrow {PQ}  \cdot \left( {D \times E} \right)} \right|}}<br />
{{\left\| {D \times E} \right\|}}} \right].

    In this question  D = \left\langle {7, - 1, - 2} \right\rangle \;\& \,E = \left\langle {1,1,2} \right\rangle
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