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Math Help - Finding parametric scalar equations of lines which are parallel to a plane

  1. #1
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    Finding parametric scalar equations of lines which are parallel to a plane

    The question: Let pi be the plane 2x-3y-6z=6 and M be the point of intersection of the plane with the y axis. Find parametric scalar equations of the line m which lies on the plane pi, passes through the point M and m is parallel to the xz plane.
    My attempt:
    M must be (o,-2,0)
    And i know the eqn of a parametric vector eqn of a line is r=r0+tv

    Where c will not have a y component. Am i right in then solving the line x+Z-2=0
    with 2x-3y-6z to find the vector? Then the line will be r=-2j=t(v)
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  2. #2
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    Ref http://www.mathhelpforum.com/math-he...wo-planes.html

    • Line is parallel to plane x-z, then Line perpendicular y-axis, \vec{e}_2
    • Line lies on plane P, then Line perpendicular \vec{v}_p\begin{bmatrix}2\\-3\\-6\end{bmatrix}
    • M(0,-2,0)
    • Line normal vector \vec{v}=\ker[\vec{e}_2,\vec{v}_p]=\ker\begin{bmatrix}2&-3&-6\\0 &1 &0\end{bmatrix}=\begin{bmatrix}3\\0\\1\end{bmatrix  }
    • Line equation \frac{x}{3}=\frac{z}{1},~y=-2
      .
    • Or \vec{x} = t\vec{v}+\vec{m}
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