demo3.py

Created on December 09, 2021

526 Bytes

A est un point de l’espace et 
−→n est un vecteur non nul. 
L’ensemble des points M de
l’espace tels que −−→AM*−→n = 0 
est le plan P passant par A et de
vecteur normal −→n .

Demo3

Soit B le point tel que →AB=→n
H le projeté orthogonal de M sur (AB)
→AM*→n=→AM*→AB=AHxAB
Ainsi, →AM*→n=0 <=> →AH*→AB=0
                <=>AHxAB=0
                <=>AH=0
Ainsi, →AM*→n=0 <=>A=H
SSI A est le projeté orthogonal 
de M sur (AB)
Ainsi, l'ensemble des points cherchés *
est le plan P orthogonal à n passant 
par A.

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