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Topic: Plane equation
Replies: 3   Last Post: Oct 17, 2007 11:35 AM

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jw12jw12jw12@yahoo.com

Posts: 37
Registered: 10/27/05
Re: Plane equation
Posted: Oct 17, 2007 11:30 AM
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On Oct 17, 11:03 am, Eoghan <lucaga...@gmail.com> wrote:
> Hi all!
> How know that the cartesian equation of a plane by three points is ax
> +by+cz+d=0, where a,b,c are the components of a normal vector. But,
> how can I pass to the parametric equation X=P?+t(P?-P?)+s(P?-P?),
> wihout using matrices?


(a,b,c) is a normal to the plane. Two vectors genertaing the plane
must be orthogonal to the normal. For example (b,-a,0) and (c,0,-a). A
point on the plane would be the x intercept (-d/a,0,0). So an equation
of the plane would be X=(-d/a,0,0)+s(b,-a,0)+t(c,0,-a).
This particular solution won't be valid in all cases (for example, if
a=0 there is no x intercept). But if you understand the basic
principle you can apply it in any particular case.




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