Parametric Equation of a Normal

**Spimon** · October 15th 2007, 09:26 PM

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

**Jhevon** · October 15th 2007, 09:54 PM

Originally Posted by Spimon

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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