 \vec{ u } -  \vec{ v } 

 \vec{ v } -  \vec{ u } 

 \vec{ u } +  \vec{ v } 

démarche

démarche

démarche

u+v

u-v

v-u

Produit scalaire

B = (4, -2)
A = (0, 0)
u = Vector(A, B)
C = (2.984791398693648, 4.391688187539614)
v = Vector(A, C)
w: u + v
D = Point(w)
E = Point(w)
a = Segment(D, E)
z = Vector(D, A)
D' = Translate(D, z)
Somme = Translate(E, z)
a' = Segment(D', Somme)
b = Vector(A, Somme)
c: u - v
F = Point(c)
d = Vector(F, A)
G = Point(c)
e = Segment(F, G)
F' = Translate(F, d)
Soustraction = Translate(G, d)
e' = Segment(F', Soustraction)
f = Vector(A, Soustraction)
g: v - u
H = Point(g)
I = Point(g)
h = Segment(H, I)
H' = Translate(H, z)
I' = Translate(I, z)
h' = Segment(H', I')
i = Vector(A, I')
m = Segment(A, C)
A'_1 = Translate(A, u)
C'_1 = Translate(C, u)
m'_1 = Segment(A'_1, C'_1)
n = Vector(B, C'_1)
o = false
A'_2 = Translate(A, u)
C' = Translate(C, u)
m' = Segment(A'_2, C')
A''_1 = Mirror(A'_2, B)
C'' = Mirror(C', B)
m'' = Segment(A''_1, C'')
p = Vector(B, C'')
q = false
r = Segment(A, B)
A' = Translate(A, v)
B' = Translate(B, v)
r' = Segment(A', B')
A'' = Mirror(A', C)
B'' = Mirror(B', C)
r'' = Segment(A'', B'')
s = Vector(C, I')
t = false
xu: x(u)
yu: y(u)
xv: x(v)
yv: y(v)
texte6: "\vec{ u } +  \vec{ v } = " + u + " + " + v + " = (" + xu + " + " + xv + " , " + yu + " + " + yv + ") = " + Somme + ""
texte7: "\vec{ u } -  \vec{ v } = " + u + " - " + v + " = (" + xu + " - " + xv + " , " + yu + " - " + yv + ") = " + Soustraction + ""
texte8: "\vec{ v } -  \vec{ u } = " + v + " - " + u + " = (" + xv + " - " + xu + " , " + yv + " - " + yu + ") = " + i + ""
texte4: "Coordonnées \vec{ u } = " + u + ""
texte5: "Coordonnées \vec{ v } = " + v + ""
j = false
k = false
l = false
α = Angle(C, A, B)
a_1: (a * cos(α))
longueurv = Distance(A, C)
longueuru = Distance(A, B)
prodscalaire: ((longueuru * longueurv) * cos(α))
b_1 = false
texte9: " \vec{ u } ∙  \vec{ v } = ∥ \vec{ u } ∥∥ \vec{ v } ∥cos α = " + (LaTeX[longueuru]) + " ∙ " + (LaTeX[longueurv]) + " ∙ cos " + (LaTeX[α]) + " = " + (LaTeX[prodscalaire]) + ""