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Math Help - Parametric equation

  1. #1
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    Parametric equation

    Let L be the line given by x = 2 - t, y = 1 + t, z = 1 + 2t. L intersects the plane 2x + y - z = 1 at the point P = (1,2,3). Find the parametric equations for the line through P which lies in the plane and is perpendicular to L.

    Im lost here. I cant find an examples on how to do this problem. I have come up with this so far

    x = 1 + at
    y = 2 + bt
    z = 3 + ct

    but Im not sure that this is right.
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  2. #2
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    Quote Originally Posted by kenshinofkin View Post
    Let L be the line given by x = 2 - t, y = 1 + t, z = 1 + 2t. L intersects the plane 2x + y - z = 1 at the point P = (1,2,3). Find the parametric equations for the line through P which lies in the plane and is perpendicular to L.

    Im lost here. I cant find an examples on how to do this problem. I have come up with this so far

    x = 1 + at
    y = 2 + bt
    z = 3 + ct

    but Im not sure that this is right.
    You are on the right track so far. A line in a plane (call it M) must be perpendicular to the plane's normal vector. We are told that the line M is also perpendicular to L. Since we know that lines lie along vectors, we can find the cross product of a normal vector of the plane and a vector pointing in the direction of line L, which will be a vector pointing in the direction of line M. You can use this to create your parametric equations and find appropriate values for a, b, and c.
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  3. #3
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    So the normal vector for the plane would be <2,1,-1>? And I would do the cross product of <2,1,-1>X<-1,1,2>?
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