# Parametric Equation of a Normal

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• Oct 15th 2007, 09:26 PM
Spimon
Parametric Equation of a Normal
I've need help finding the parametric equation for the normal to following function.

http://img148.imageshack.us/img148/4976/functiontg3.jpg

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 (Doh). Any help would be greatly appreciated!

Thanks

- Simon
• Oct 15th 2007, 09:54 PM
Jhevon
Quote:

Originally Posted by Spimon
I've need help finding the parametric equation for the normal to following function.

http://img148.imageshack.us/img148/4976/functiontg3.jpg

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 (Doh). Any help would be greatly appreciated!

Thanks

- Simon

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

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

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

or

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