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Math Help - Parametric Equations for a Line

  1. #1
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    Parametric Equations for a Line

    Given that a, b, and c are not all zero, find parametric equations
    for a line in R3 that passes through the point (x0, y0, z0)
    and is perpendicular to the line
    x = x0 + at, y = y0 + bt, z = z0 + ct
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  2. #2
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    Re: Parametric Equations for a Line

    Quote Originally Posted by Civy71 View Post
    Given that a, b, and c are not all zero, find parametric equations
    for a line in R3 that passes through the point (x0, y0, z0)
    and is perpendicular to the line
    x = x0 + at, y = y0 + bt, z = z0 + ct

    Find any vector <\alpha,\beta.\gamma> such that a\cdot\alpha+b\cdot\beta+c\cdot\gamma=0.

    Then the line is <x_0,y_0,z_0>+t<\alpha,\beta.\gamma>.
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    Re: Parametric Equations for a Line

    Quote Originally Posted by Plato View Post
    Find any vector <\alpha,\beta.\gamma> such that a\cdot\alpha+b\cdot\beta+c\cdot\gamma=0.

    Then the line is <x_0,y_0,z_0>+t<\alpha,\beta.\gamma>.
    such a vector is (0,0,1)X(a,b,c), which is perpendicular to (a,b,c)
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