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Math Help - Parametric Equation of a Normal

  1. #1
    Junior Member Spimon's Avatar
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    Parametric Equation of a Normal

    I've need help finding the parametric equation for the normal to following function.



    Is there a formula or general form of the parametric equation for a normal line?
    I can only find info on circles in 2 dimensions . Any help would be greatly appreciated!

    Thanks

    - Simon
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Spimon View Post
    I've need help finding the parametric equation for the normal to following function.



    Is there a formula or general form of the parametric equation for a normal line?
    I can only find info on circles in 2 dimensions . Any help would be greatly appreciated!

    Thanks

    - Simon
    the normal line to a curve F(x,y,z) at the point (x_0,y_0,z_0) is given by:

    \boxed{ x = x_0 + tF_x(x_0,y_0,z_0) \mbox { , }y = y_0 + tF_y(x_0,y_0,z_0) \mbox { , } z = z_0 + tF_z(x_0,y_0,z_0) } ----> Parametric equation of normal line

    where t is a parameter, and F_x(x_0,y_0,z_0), F_y(x_0,y_0,z_0), \mbox { and } F_z(x_0,y_0,z_0) are the partial derivatives of F with respect to x,y, \mbox { and }z respectively, evaluated at the point (x_0,y_0,z_0)

    or

    \boxed { \frac {x - x_0}{F_x(x_0,y_0,z_0)} = \frac {y - y_0}{F_y(x_0,y_0,z_0)} = \frac {z - z_0}{F_z(x_0,y_0,z_0)}} -----> Symmetric equation of normal line
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