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.