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Math Help - Parametric line equation and relationship to a plane

  1. #1
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    Parametric line equation and relationship to a plane

    I have a plane that has an equation of 2x - y + z = 7

    My parametric equations for a line L, are

    x = - 1 + t

    y = 2 + t

    z = 1 + 3t

    Are these perpendicular to each other, or is line in the plane...
    Please someone give me a push in the right direction. Thanks Frostking
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  2. #2
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    Quote Originally Posted by Frostking View Post
    I have a plane that has an equation of 2x - y + z = 7

    My parametric equations for a line L, are

    x = - 1 + t

    y = 2 + t

    z = 1 + 3t

    Are these perpendicular to each other, or is line in the plane...
    Please someone give me a push in the right direction. Thanks Frostking

    So the line is (-1,2,1) + t(1,1,3) ==> since the director vector (1,1,3) is not perpendicular to the given plane (for this the vector would have to be in the same direction as the plane's normal (2,-1,1), the line isn't perpendicular to the plane, but it crosses it: just plug the parametric values of x,y,z into the plane's eq. and find which t solves the equation.

    Tonio
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