coordoneeprojorthopointsurdroite.py

Created on March 23, 2021

616 Bytes

# Type your text here

A(1-21) B(-2-15) C (-15-104)
determiner les coordonnées du point
H ortho du point C sur la droite 
(AB)

AB() 
une representation para de la droite
AB passant par A et de vecteur 
directeur AB est:
  1-3t
  -2+1t avec t reel
  1+4t

le point H appartient a AB donc 
ces coordonnnes verifient le 
equations du systeme para de la 
droite AB on a ainsi:
  H(1-3t,-2+t,1+4t)
  CH()
  
or CH et AB sont ortho donc 
CH.AB=0
AB()
(16-3t)*-3+1(8+t)+4(-3+4t)=0
t=2

le point H est le projeté ortho 
de C sur AB a donc pour coordone
H(1-3*2,-2+2,1+4*2)(-5,0,9)

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