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Math Help - Find equation of Line where Plane Meets

  1. #1
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    Find equation of Line where Plane Meets

    Find the equations for the line of intersctions of the planes:

    x+y+z=1
    x+y=2

    I worked it out to be r(t)=3i-j-k+t(i-j)


    The ans says:
    r(t)=2j-k+t(-i+j)
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  2. #2
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    Can you show your work, please?
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  3. #3
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    x+y+z=1
    x+y=2
    let x=t
    t+y+z=1
    y=1-t-z
    solving for x we get
    x=3+t
    now solving for y we get
    y=-1-t
    now solving forz we get
    z=-1
    therefore r(t)=3i-j-k+t(i-j)
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  4. #4
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    Hmm. There's something wrong with your method if x = t and x = 3 + t. That's impossible, isn't it? I would suggest row reducing your augmented matrix thus:

    \left[\begin{array}{rrr|r}<br />
1 &1 &1 &1\\<br />
1 &1 &0 &2<br />
\end{array}\right]\to\dots

    You should get a one-parameter family of solutions. What do you get?
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  5. #5
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    Thanks I just realised that mistake!
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  6. #6
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    So what do you get now?
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  7. #7
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    I get:

    r(t)=2j-k+t(-i+j)

    Which is the published ans.
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  8. #8
    A Plied Mathematician
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    Jolly good.
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