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Math Help - Find parametric equation

  1. #1
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    Find parametric equation

    I have an odd problem in the book where i have no solution to and i am not sure if i am doing it correctly.

    Let L be the line given by x = 3-t, y=2+t, z= -4 +2t

    L intersects the plane 3x-2y+z=1 at the point P=(3, 2, -4)

    Find parametric equations for the line through P which lies in the plane and is perpendicular to L

    Attempt:

    Direction Vector v = <-1,1,2>

    Normal Vector n = <3, -2, 1>

    v \times n = <5, 7, -1>

    X = P + vt

    Point: P=(3, 2, -4)
    v = <-1,1,2>

    putting it together

    (3, 2, -4) + <-1,1,2>t

    Parametric equation: x = 3-t, y = 2+t , z = -4 +2t

    Somehow, i dont think this is correct?

    Thank you
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  2. #2
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    Re: Find parametric equation

    Quote Originally Posted by icelated View Post
    I have an odd problem in the book where i have no solution to and i am not sure if i am doing it correctly.
    Let L be the line given by x = 3-t, y=2+t, z= -4 +2t
    L intersects the plane 3x-2y+z=1 at the point P=(3, 2, -4)
    Find parametric equations for the line through P which lies in the plane and is perpendicular to L
    Attempt:
    Direction Vector v = <-1,1,2>
    Normal Vector n = <3, -2, 1>
    v \times n = <5, 7, -1>
    X = P + vt
    Point: P=(3, 2, -4)
    v = <-1,1,2>
    putting it together
    (3, 2, -4) + <-1,1,2>t
    Parametric equation: x = 3-t, y = 2+t , z = -4 +2t
    Somehow, i dont think this is correct?
    You have a mistake in concept. Your line is
    \\x=3+5t\\y=2+7t\\z=-4-t

    WHY?
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  3. #3
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    Re: Find parametric equation

    Are you saying i should use
    x = P + (v \times n) t

    instead of

    X = P + vt
    Last edited by icelated; May 2nd 2013 at 02:56 PM.
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  4. #4
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    Re: Find parametric equation

    Quote Originally Posted by icelated View Post
    I dont know what you mean. What you are trying to get.Are you saying i should use v X n instead of v?
    Can you read?

    You posted: Parametric equation: \color{red}x = 3-t, y = 2+t , z = -4 +2t
    THAT IS INCORRECT!

    THIS IS CORRECT: Parametric equation: x = 3+5t,~ y = 2+7t ,~ z = -4 -t.

    Then I asked you why that is correct?
    Thanks from icelated
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