\vec{u}

\vec{v}

\vec{v}

Avec les coordonnées.

Avec les normes et angles

A

H

B

Avec le projeté orthogonal

B = (0, 5)
D = (4, 0)
C = (1, -1)
v = Vector(C, D)
A = (-1, 2)
u = Vector(A, B)
A' = Translate(A, v)
w = Vector(A, A')
m, n, q, r, poly2, text18 = AngleOriente(A, u, w)
h = Line(A, v)
i = OrthogonalLine(B, h)
H = Intersect(h, i)
dah = Distance(A, H)
sig: cos(Angle[H, A, A'])
p: u v
E = Midpoint(A, B)
F = Midpoint(A', A)
G = Midpoint(C, D)
text4: "\vec{u}.\vec{v}=" + p
text5: "x_\vec{u}.x_\vec{v}+y_\vec{u}.y_\vec{v}=" + (x(u)) + "\,x\," + (x(v)) + "\,+\," + (y(u)) + "\,x\," + (y(v)) + "=" + (x(u) x(v)) + "\,+\," + (y(u) y(v)) + "=" + p
nu = Length(u)
nv = Length(v)
l: Min[nu, nv] / 3
a = Segment(A, B)
b = Segment(A, A')
text7: "\vec{u} \left(\array{" + (x(u)) + "\\" + (y(u)) + "}\right)"
text8: "\vec{v} \left(\array{" + (x(v)) + "\\" + (y(v)) + "}\right)"
text10: "||\vec{u}||.||\vec{v}||.cos(\vec{u},\vec{v})=" + nu + "\, x \," + nv + "\, x \," + (cos(m)) + " \, = \," + p
f = false
g = false
j = Segment(B, H)
A'_1 = Translate(A, v)
k = false
dab = Distance(A, A')
text17: "\overline{AH}.\overline{AB}=" + (sig dah) + "\; x \; " + dab + "=" + p
I = (2, 4)
text9: "(\vec{u},\vec{v})=" + m

Tool: Angle Orienté de vecteurs (origine-vecteur-vecteur) (command AngleOriente)
Origine des représentants, 1er vecteur, 2ème vecteur
Input: O, u, v
Output: mes_θ, u', v', c, Flèche, E_θ

θ = Angle(u, v)
mes_θ: (sgn(sin(θ)) + If[sin(θ) ≟ 0, 1, 0]) acos(cos(θ))
A = Translate(O, u)
B = Translate(O, v)
u' = Vector(O, A)
v' = Vector(O, B)
k: Min[1, Length[v'] / Length[u']] / 4
F_0 = Translate(O, Vector[k u'])
F' = Rotate(F_0, (0.5 + 3 abs(mes_θ) / (8 * 3.14)) mes_θ, O)
F = Rotate(F_0, mes_θ, O)
L = Rotate(F', 14.999999999999998°, F)
E = Rotate(F', 345°, F)
c = CircumcircleSector(F_0, F', F)
Flèche, e, f, l = Polygon(F, L, E)
E_θ: mes_θ + " rad"