%@AUTEUR: David Nivaud

verbatimtex 
%&latex 
\documentclass[12pt]{article} 
\def\vect#1{\overrightarrow{#1}} 
\def\Vect#1{\overrightarrow{\strut #1}} 
\everymath{\displaystyle} 
\begin{document} 
etex 
 

beginfig(1); 
%repere cartesien dans l'espace 
numeric u; 
pair t,s,q; 
u = 1cm; 
 
%definitions de l'origine et des vecteurs de base 
t=(2u,0u); 
s=(0u,2u); 
q=(-1u,-1.5u); 
z0 = (0,0); 
z1= z0 shifted t; 
z2 = z0 shifted s; 
z3 = z0 shifted q; 
 
%trace de l'origine et des vecteurs de base 
dotlabel.lft(btex $O$ etex, z0); 
label.bot(btex $\vect{\jmath}$ etex, z1); 
label.lft(btex $\vect{\imath}$ etex, z3); 
label.lft(btex $\vect{k}$ etex, z2); 
 
%trace des axes 
drawarrow z0--z1 ; 
drawarrow z0--z2 ; 
drawarrow z0--z3 ; 
 
endfig; 
 
 
 

beginfig(2); 
% coordonnées d'un point dans un repere de l'espace 
numeric u; 
pair t,s,q; 
u = 1cm; 
 
%definitions de l'origine et des vecteurs de base 
t=(1u,0u); 
s=(0u,1u); 
q=(-0.5u,-0.5u); 
z0 = (0,0); 
z1= z0 shifted t; 
z2 = z0 shifted s; 
z3 = z0 shifted q; 
 
%trace de l'origine et des vecteurs de base 
dotlabel.lft(btex $O$ etex, z0); 
label.bot(btex $\vect{\jmath}$ etex, z1); 
label.lft(btex $\vect{\imath}$ etex, z3); 
label.lft(btex $\vect{k}$ etex, z2); 
 
%trace des axes 
drawarrow z0--z1 ; 
drawarrow z0--z2 ; 
drawarrow z0--z3 ; 
 
%construction du point M 
z4 = z0 shifted 4t; 
z5 = z0 shifted 4s; 
z6 = z0 shifted 4q; 
drawarrow z0--z4 ; 
drawarrow z0--z5 ; 
drawarrow z0--z6 ; 
z7= 3.5t+2.5q; 
label.bot(btex $M'$ etex, z7); 
z8 = 3.5t ; 
z9 = 2.5q ; 
draw z7--z8 dashed evenly; 
draw z7--z9 dashed evenly; 
label.top(btex $y$ etex, z8); 
label.lft(btex $x$ etex, z9); 
z10 = z7 shifted 3s; 
draw z7--z10 dashed evenly; 
label.rt(btex $M$ etex, z10); 
z11 = z10 shifted z0-z7; 
draw z11--z10 dashed evenly; 
label.lft(btex $z$ etex, z11); 
drawarrow z0--z10; 
drawarrow z0--z7; 
 
endfig; 
 

beginfig(3); 
%illustration du calcul de distance dans un repere orthonormal 
numeric u; 
pair t,s,q; 
u = 1cm; 
 
%definitions de l'origine et des vecteurs de base 
t=(1u,0u); 
s=(0u,1u); 
q=(-0.5u,-0.5u); 
 
%construction de l'origine et des vecteurs de base 
z0 = (0,0); 
z1= z0 shifted t; 
z2 = z0 shifted s; 
z3 = z0 shifted q; 
dotlabel.lft(btex $O$ etex, z0); 
label.bot(btex $\vect{\jmath}$ etex, z1); 
label.lft(btex $\vect{\imath}$ etex, z3); 
label.lft(btex $\vect{k}$ etex, z2); 
 
%trace des axes 
drawarrow z0--z1 ; 
drawarrow z0--z2 ; 
drawarrow z0--z3 ; 
 
%construction du point M et de ses projetes 
z4 = z0 shifted 4t; 
z5 = z0 shifted 4s; 
z6 = z0 shifted 4q; 
drawarrow z0--z4 ; 
drawarrow z0--z5 ; 
drawarrow z0--z6 ; 
z7= 3.5t+2.5q; 
label.bot(btex $m$ etex, z7); 
z8 = 3.5t ; 
z9 = 2.5q ; 
draw z7--z8 dashed evenly; 
draw z7--z9 dashed evenly; 
label.top(btex $b$ etex, z8); 
label.lft(btex $a$ etex, z9); 
z10 = z7 shifted 3s; 
draw z7--z10 dashed evenly; 
label.rt(btex $M$ etex, z10); 
z11 = z10 shifted z0-z7; 
draw z11--z10 dashed evenly; 
label.lft(btex $c$ etex, z11); 
drawarrow z0--z10; 
drawarrow z0--z7; 
 
endfig;
end