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Thread: 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 $\displaystyle x = 3-t, y=2+t, z= -4 +2t$

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

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

    Attempt:

    Direction Vector v = $\displaystyle <-1,1,2>$

    Normal Vector n = $\displaystyle <3, -2, 1>$

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

    $\displaystyle X = P + vt$

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

    putting it together

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

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

    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 $\displaystyle x = 3-t, y=2+t, z= -4 +2t$
    L intersects the plane $\displaystyle 3x-2y+z=1$ at the point $\displaystyle P=(3, 2, -4)$
    Find parametric equations for the line through P which lies in the plane and is perpendicular to L
    Attempt:
    Direction Vector v = $\displaystyle <-1,1,2>$
    Normal Vector n = $\displaystyle <3, -2, 1>$
    $\displaystyle v \times n = <5, 7, -1>$
    $\displaystyle X = P + vt$
    Point: $\displaystyle P=(3, 2, -4)$
    v = $\displaystyle <-1,1,2>$
    putting it together
    $\displaystyle (3, 2, -4) + <-1,1,2>t$
    Parametric equation: $\displaystyle x = 3-t, y = 2+t , z = -4 +2t$
    Somehow, i dont think this is correct?
    You have a mistake in concept. Your line is
    $\displaystyle \\x=3+5t\\y=2+7t\\z=-4-t$

    WHY?
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  3. #3
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    Re: Find parametric equation

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

    instead of

    $\displaystyle X = P + vt$
    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: $\displaystyle \color{red}x = 3-t, y = 2+t , z = -4 +2t$
    THAT IS INCORRECT!

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

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