 \vec{ u } 

 \vec{ v } 

 \vec{ w } 

 \vec{ s } 

Choisir vos vecteurs

Choisir les coefficients multiplicateurs

Construisons

Voir les étapes :

on peut les déplacer en “attrapant” les extrêmités

Représenter une combinaison linéaire de trois vecteurs

Source initiale : http://dmentrard.free.fr/GEOGEBRA/

a = 2.1 (slider from -5 to 5, step 0.1)
b = -1.4 (slider from -5 to 5, step 0.1)
c = 0.9 (slider from -5 to 5, step 0.1)
A = (-2.836755400696864, 6.18326968641115)
B = (-0.2858334587688768, 7.536027837398372)
u = Vector(A, B)
C = (-3.006675029036005, -0.11550476190476189)
D = (-3, -3)
v = Vector(C, D)
E = (-3, 4)
F = (1, 2)
w = Vector(E, F)
G = (7, -1)
H = Translate(G, Vector[(a * u)])
I = Translate(H, Vector[(b * w)])
J = Translate(I, Vector[(c * v)])
d = Segment(A, B)
z = Vector(A, G)
A' = Translate(A, z)
B' = Translate(B, z)
e = Segment(A', B')
f = Segment(E, F)
g = Vector(E, H)
E' = Translate(E, g)
F' = Translate(F, g)
h = Segment(E', F')
i = Vector(C, I)
j = Segment(C, D)
C' = Translate(C, i)
D' = Translate(D, i)
k = Segment(C', D')
l = Vector(G, H)
m = Vector(H, I)
n = Vector(I, J)
p = Vector(G, J)
K = Midpoint(A, B)
L = Midpoint(E, F)
M = Midpoint(C, D)
N = Midpoint(G, H)
T4: "" + a + "  \; \vec{ u } "
T5: "" + b + " \; \vec{ v } "
T6: "" + c + " \; \vec{ w } "
O = Midpoint(H, I)
P = Midpoint(I, J)
Q = Midpoint(G, J)
T8: " \vec{ s } \;  = \;  " + a + ". \; \vec{ u }  \; + \; " + b + ". \; \vec{ v } \; + \;  " + c + ". \; \vec{ w } "
t = 4 (slider from 0 to 4, step 1)