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Math Help - Line of intersection of two planes

  1. #1
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    Line of intersection of two planes

    2x+3y-5z=0
    3x-y+2z=0

    I have found the direction vector using the vector product. The answer in the book says the lines goes through point (2,1,1). I think the 0's are a misprint. How do I find that the line goes though that point?
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  2. #2
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    Re: Line of intersection of two planes

    Quote Originally Posted by Stuck Man View Post
    2x+3y-5z=0
    3x-y+2z=0
    I have found the direction vector using the vector product. The answer in the book says the lines goes through point (2,1,1). I think the 0's are a misprint. How do I find that the line goes though that point?
    That is indeed a misprint. The line must be a subset of both planes. That point is on neither plane.
    The obvious point to pick is (0,0,0).
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  3. #3
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    Re: Line of intersection of two planes

    Is it possible to figure out what the constants should be?
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    Re: Line of intersection of two planes

    Quote Originally Posted by Stuck Man View Post
    Is it possible to figure out what the constants should be?
    I have no idea what "the constants should be" could mean.
    The line is \left\{ \begin{gathered}  x(t) = t \hfill \\  y(t) =  - 19t \hfill \\  z(t) =  - 11t \hfill \\ \end{gathered}  \right.
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  5. #5
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    Re: Line of intersection of two planes

    The zeroes. If I put the point (2,1,1) into the plane equations I get -4 for the first constant and 7 for the other.
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  6. #6
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    Re: Line of intersection of two planes

    Quote Originally Posted by Stuck Man View Post
    The zeroes. If I put the point (2,1,1) into the plane equations I get -4 <-- that should be 2
    for the first constant and 7 for the other.
    The planes p_1: 2x+3y-z=2 and p_2: 3x-y+2z = 7 have the line of interception

    l:\left \{ \begin{array}{l}x=-t+\frac{23}{11} \\ y=19t - \frac8{11} \\ z= 11t\end{array}\right. With t=\frac1{11} you'll get the point (2,1,1)
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  7. #7
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    Re: Line of intersection of two planes

    Yes, thanks.
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