demo4.py

Created by ramadiallo01

Created on December 10, 2021

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Propriété 2. Dans l’espace muni 
d’un repère orthonormé 
(O;i,j,k)
• on considère le vecteur −→n (a;b;c)
 et un point A(xA; yA; zA). 
 Le plan P qui passe par le point
A et de vecteur normal −→n a pour
équation cartésienne 
: ax + by + cz + d = 0 avec d =
−(axA + byA + czA)

• Réciproquement, a,b,c,d étant 4
nombres réels données avec a,b,c
non tous nuls ; l’ensemble
des points M(x; y; z) tels que 
ax + by + cz = 0 est un plan de
vecteur normal −→n (a;b;c)


Demonstration 4
Soit A(Xa,Ya,Za) et−→n (a;b;c)
→n est orthogonal à P
M(x;y;z)∈P SSI AM*n=0 
SSI a(Xm-Xa)+b(Ym-Ya)+c(Zm-Za) =0
SSI ax+by+cz-(aXa+bYa+cZa)=0
SSI ax+by+cz+d=0
avec d=-(aXa+bYa+cZa)

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