%@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); 
%Representants d'un vecteur 
numeric u; 
pair t; 
u = 1cm; 
t=(1u,2u); 
transform T; 
T = identity shifted t; 
z0 = (0,0); z1= z0 transformed T; 
z2 = (2u,0); z3 = z2 transformed T; 
z4 = (3u,-1u); z5 = z4 transformed T; 
drawarrow z0--z1 ; 
drawarrow z2--z3 ; 
drawarrow z4--z5 ; 
label.lft(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.lft(btex $C$ etex, z2); 
label.rt(btex $D$ etex, z3); 
label.lft(btex $E$ etex, z4); 
label.rt(btex $F$ etex, z5); 
label.bot(btex $\vect{u}$ etex, 0.5[z0,z1]); 
label.bot(btex $\vect{u}$ etex, 0.5[z2,z3]); 
label.bot(btex $\vect{u}$ etex, 0.5[z4,z5]); 
endfig; 
 
 
 
beginfig(2); 
%egalité de deux vecteurs et parallelogramme 
numeric u; 
pair t; 
u = 1cm; 
t=(1u,2u); 
transform T; 
T= identity shifted t; 
z0 = (0,0);z1 = z0 transformed T; 
z2=(3u,-1u);z3=z2 transformed T ; 
drawarrow z0--z1 withcolor red; 
drawarrow z2--z3 withcolor red; 
draw z0--z2 dashed evenly; 
draw z1--z3 dashed evenly; 
label.lft(btex $A$ etex, z0); 
label.top(btex $B$ etex, z1); 
label.bot(btex $C$ etex, z2); 
label.rt(btex $D$ etex, z3); 
endfig; 
 
beginfig(3); 
%addition de deux vecteurs(Chasles) 
numeric u; 
pair t,r; 
u=1cm; 
t=(2u,1u); 
r=(3u,-2u); 
transform T,R; 
T= identity shifted t; 
R= identity shifted r; 
z0=(0,0);z1= z0 transformed T; 
z2=z1 transformed R; 
drawarrow z0--z1 withcolor green; 
drawarrow z1--z2 withcolor green; 
drawarrow z0--z2 withcolor red; 
label.lft(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.rt(btex $C$ etex, z2); 
label.top(btex $\vect{u}$ etex, 0.5[z0,z1]); 
label.top(btex $\vect{v}$ etex, 0.5[z1,z2]); 
label.bot(btex $\vect{u}+\vect{v}$ etex, 0.5[z0,z2]); 
endfig; 
 
beginfig(4); 
%addition de deux vecteurs(parallelogramme) 
numeric u; 
pair t,r,s; 
u=1cm; 
t=(2u,1u); 
r=(-2u,2u); 
transform T,R; 
T= identity shifted t; 
R= identity shifted r; 
z0=(0,0);z1= z0 transformed T; 
z2=z0 transformed R;z3=z1 transformed R; 
drawarrow z0--z1 withcolor green; 
drawarrow z0--z2 withcolor green; 
drawarrow z0--z3 withcolor red; 
label.bot(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.lft(btex $D$ etex, z2); 
label.top(btex $C$ etex, z3); 
label.bot(btex $\vect{u}$ etex, 0.5[z0,z1]); 
label.bot(btex $\vect{v}$ etex, 0.5[z0,z2]); 
label.rt(btex $\vect{u}+\vect{v}$ etex, 0.7[z0,z3]); 
endfig; 
 
 
beginfig(5); 
%soustraction de deux vecteurs 
numeric u; 
pair t,r,s; 
u=1cm; 
t=(2u,1u); 
r=(2u,-1.5u); 
transform T,R,S; 
T= identity shifted t; 
R= identity shifted -r; 
S= identity shifted r; 
z0=(0,0);z1= z0 transformed T; 
z2=z1 transformed R; 
drawarrow z0--z1 withcolor green; 
drawarrow z1--z2 withcolor green; 
drawarrow z0--z2 withcolor red; 
label.bot(btex $\vect{u}$ etex, 0.5[z0,z1]); 
label.rt(btex $-\vect{v}$ etex, 0.5[z1,z2]); 
label.lft(btex $\vect{u}-\vect{v}$ etex, 0.5[z0,z2]); 
z4=(-2u,2u);z5=z4 transformed T; 
z6=(-3u,1u); z7=z6 transformed S; 
drawarrow z4--z5 withcolor blue; 
drawarrow z6--z7 withcolor blue; 
label.top(btex $\vect{u}$ etex, 0.5[z4,z5]); 
label.rt(btex $\vect{v}$ etex, 0.5[z6,z7]); 
endfig; 
 
 
beginfig(6); 
numeric u,a,b; 
%multiples d'un vecteur 
pair t; 
u = 1cm; 
t=(1u,2u); 
transform T,R,S; 
T = identity shifted t; 
R = identity shifted 2t; 
S = identity shifted -1.5t; 
z0 = (0,0); z1= z0 transformed T; 
z2 = (-2.5u,0); z3 = z2 transformed R; 
z4 = (3u,3u); z5 = z4 transformed S; 
drawarrow z0--z1 ; 
drawarrow z2--z3 ; 
drawarrow z4--z5 ; 
label.rt(btex $\vect{u}$ etex, 0.5[z0,z1]); 
label.rt(btex $k\vect{u} \, (k>0)$ etex, 0.5[z2,z3]); 
label.rt(btex $k\vect{u} \, (k<0)$ etex, 0.5[z4,z5]); 
endfig; 
 
beginfig(7); 
%colinearite de deux vecteurs et directions paralleles 
numeric u; 
pair t,r; 
u=1cm; 
t=(2u,3u); 
r=(-1u,-1.5u); 
transform T,R; 
T= identity shifted t; 
R= identity shifted r; 
z0=(0,0);z1= z0 transformed T; 
z2=(2u,2u);z3=z2 transformed R; 
drawarrow z0--z1; 
drawarrow z2--z3; 
label.lft(btex $A$ etex, z0); 
label.rt(btex $B$ etex, z1); 
label.rt(btex $D$ etex, z2); 
label.rt(btex $C$ etex, z3); 
label.top(btex $\vect{u}$ etex, 0.5[z0,z1]); 
label.bot(btex $\vect{v}$ etex, 0.5[z2,z3]); 
endfig; 
 
beginfig(8); 
%coordonnees d'un point dans un repere cartesien du plan 
numeric u; 
pair i,j; 
u=0.7cm; 
 
%definition de l'origine et des vecteurs de base 
i=(2u,0u); 
j=(0.2u,1u); 
transform T,R; 
T= identity shifted i; 
R= identity shifted j; 
z0=(0,0);z1= z0 transformed T; 
z2=z0 transformed R; 
 
%trace des axes et de l'origine et des vecteurs de base 
drawarrow z0--z1 ; 
drawarrow z0--z2 ; 
label.llft(btex $O$ etex, z0); 
label.bot(btex $\vect{i}$ etex, 0.5[z0,z1]); 
label.lft(btex $\vect{j}$ etex, 0.5[z0,z2]); 
 
%trace des projections et des pointilles 
z3= z0 shifted 3i;z4= z0 shifted -i; 
z5= z0 shifted 4j; z6= z0 shifted -j; 
z7 = z0 shifted 3i+4j; 
draw z4--z3+i withcolor blue; draw z6--z5+j withcolor blue; 
drawarrow z0--z7 withcolor green; 
label.rt(btex $M$ etex, z7); 
draw z7--z3 dashed evenly; 
draw z7--z5 dashed evenly; 
label.rt(btex $\Vect{OM}=x\vect{i}+y\vect{j}$ etex, 0.3[z0,z7]); 
label.bot(btex $x$ etex, z3); 
label.lft(btex $y$ etex, z5); 
endfig; 
 
 
 
beginfig(9); 
%coordonnées d'un vecteur 
numeric u; 
pair i,j; 
u=0.7cm; 
 
i=(2u,0u); 
j=(0.2u,1u); 
transform T,R; 
T= identity shifted i; 
R= identity shifted j; 
z0=(0,0); 
z33= z0 shifted 4i;z4= z0 shifted -i; 
z5= z0 shifted 4j; z6= z0 shifted -j; 
 
draw z4--z33 withcolor blue; draw z6--z5 withcolor blue; 
z7= z0 shifted i;z8 = z0 shifted j; 
label.bot(btex $\vect{j}$ etex, 0.5[z0,z7]); 
label.lft(btex $\vect{j}$ etex, 0.5[z0,z8]); 
drawarrow z0--z7; 
drawarrow z0--z8; 
 
z1=(4u,1u); 
z2=z1 shifted 1.5i; 
z3=z2 shifted 2j; 
drawarrow z1--z2 dashed evenly withcolor green; 
drawarrow z2--z3 dashed evenly withcolor green; 
drawarrow z1--z3 withcolor red; 
label.llft(btex $O$ etex, z0); 
label.bot(btex $x\vect{i}$ etex, 0.5[z1,z2]); 
label.rt(btex $y\vect{j}$ etex, 0.5[z2,z3]); 
label.lrt(btex $\vect{u}$ etex, 0.5[z1,z3]); 
z9=z0 shifted 1.5i; 
z10=z0 shifted 2j; 
z11= z0 shifted 1.5i+2j; 
draw z9--z11 dashed evenly withcolor green; 
draw z10--z11 dashed evenly withcolor green; 
drawarrow z0--z11 withcolor red; 
label.top(btex $M(x;y)$ etex, z11); 
endfig; 
 
beginfig(10); 
%coordonnees d'un vecteur AB 
numeric u; 
pair i,j; 
u=0.7cm; 
 
i=(2u,0u); 
j=(0.2u,1u); 
transform T,R; 
T= identity shifted i; 
R= identity shifted j; 
z0=(0,0); 
z4= z0 shifted 4i;z5= z0 shifted -i; 
z6= z0 shifted 4j; z7= z0 shifted -j; 
 
draw z5--z4 withcolor blue; draw z7--z6 withcolor blue; 
 
z8= z0 shifted i;z9 = z0 shifted j; 
 
label.bot(btex $\vect{j}$ etex, 0.8[z0,z8]); 
label.lft(btex $\vect{j}$ etex, 0.5[z0,z9]); 
drawarrow z0--z8; 
drawarrow z0--z9; 
 
z1=z0 shifted 0.5i+1.5j; 
z2=z1 shifted 2i; 
z3=z2 shifted 2j; 
 
drawarrow z1--z2 withcolor red; 
drawarrow z2--z3 withcolor green; 
drawarrow z1--z3 withcolor blue; 
 
label.llft(btex $O$ etex, z0); 
label.top(btex $A$ etex, z1); 
label.top(btex $B$ etex, z3); 
label.bot(btex $(x_{B}-x_{A})\vect{i}$ etex, 0.5[z1,z2]); 
label.rt(btex $(y_{B}-y_{A})\vect{j}$ etex, 0.5[z2,z3]); 
 
z10=z1 shifted -1.5j; z11= z10 shifted z2-z1; z12= z1 shifted -0.5i; 
z13= z12 shifted z3-z2; 
 
draw z1--z10 dashed evenly; 
draw z2--z11 dashed evenly; 
draw z1--z12 dashed evenly; 
draw z3--z13 dashed evenly; 
 
label.bot(btex $x_{A}$ etex, z10); 
label.bot(btex $x_{B}$ etex, z11); 
label.lft(btex $y_{A}$ etex, z12); 
label.lft(btex $y_{B}$ etex, z13); 
endfig; 
 
beginfig(11); 
%reperage sur une droite 
numeric u; 
pair t; 
u = 1cm; 
t=(1u,0u); 
transform T; 
T = identity shifted t; 
z0 = (0,0); z1= z0 transformed T; 
z2 = (-4u,0u); 
z3 = (4u,0u); 
z4 = (-2u,0u); 
 
drawarrow z0--z1 withcolor red; 
draw z2--z3 ; 
dotlabel.bot(btex $0$ etex, z0); 
dotlabel.bot(btex $1$ etex, z1); 
dotlabel.bot(btex $-2$ etex, z4); 
label.top(btex $M$ etex, z4); 
label.top(btex $0$ etex, z0); 
label.bot(btex $\vect{i}$ etex, 0.5[z0,z1]); 
endfig; 
 
beginfig(12); 
%repere cartesien dans le plan 
numeric u; 
pair i,j; 
u=1cm; 
 
i=(1u,0u); 
j=(0.2u,0.5u); 
transform T,R; 
T= identity shifted i; 
R= identity shifted j; 
z0=(0,0);z1= z0 transformed T; 
z2=z0 transformed R; 
 
drawarrow z0--z1 ; 
drawarrow z0--z2 ; 
label.llft(btex $O$ etex, z0); 
label.bot(btex $\vect{i}$ etex, 0.5[z0,z1]); 
label.lft(btex $\vect{j}$ etex, 0.5[z0,z2]); 
z3= z0 shifted 3i;z4= z0 shifted -i; 
z5= z0 shifted 3j; z6= z0 shifted -j; 
draw z4--z3+i withcolor blue; draw z6--z5+j withcolor blue; 
endfig; 
 
beginfig(13); 
%repere cartesien orthogonal dans le plan 
numeric u; 
pair i,j; 
u=1cm; 
 
i=(1u,0u); 
j=(0u,0.5u); 
transform T,R; 
T= identity shifted i; 
R= identity shifted j; 
z0=(0,0);z1= z0 transformed T; 
z2=z0 transformed R; 
 
drawarrow z0--z1 ; 
drawarrow z0--z2 ; 
label.llft(btex $O$ etex, z0); 
label.bot(btex $\vect{i}$ etex, 0.5[z0,z1]); 
label.lft(btex $\vect{j}$ etex, 0.5[z0,z2]); 
z3= z0 shifted 3i;z4= z0 shifted -i; 
z5= z0 shifted 3j; z6= z0 shifted -j; 
draw z4--z3+i withcolor blue; draw z6--z5+j withcolor blue; 
endfig; 
 
beginfig(14); 
%repere cartesien orthonormal dans le plan 
numeric u; 
pair i,j; 
u=1cm; 
 
i=(1u,0u); 
j=(0u,1u); 
transform T,R; 
T= identity shifted i; 
R= identity shifted j; 
z0=(0,0);z1= z0 transformed T; 
z2=z0 transformed R; 
 
drawarrow z0--z1 ; 
drawarrow z0--z2 ; 
label.llft(btex $O$ etex, z0); 
label.bot(btex $\vect{i}$ etex, 0.5[z0,z1]); 
label.lft(btex $\vect{j}$ etex, 0.5[z0,z2]); 
z3= z0 shifted 3i;z4= z0 shifted -i; 
z5= z0 shifted 2j; z6= z0 shifted -0.5j; 
draw z4--z3+i withcolor blue; draw z6--z5+j withcolor blue; 
endfig;
end