Exprimer  \; \vec w   \; comme  \;combinaison \; linéaire  \;de  \;\vec u \;et\; \vec v

Bouger le curseur pour voir la construction

Vous pouvez déplacer les vecteurs initiaux

\vec u

\vec w

\vec v

C = (-10.858333333333322, 0.275)
A = (-1.8166666666666664, -4.308333333333333)
v = Vector(A, C)
l = Line(A, C)
aa = 3.1 (slider from 0 to 3.1, step 0.01)
u_2: (1 + sgn(1 - aa + 0.001)) / 2
v_1: (1 + sgn(2 - aa + 0.001)) / 2
w_1: (1 + sgn(3 - aa + 0.001)) / 2
z: (1 + sgn(4 - aa + 0.001)) / 2
a2: (1 - u_2) * v_1 * w_1 * z
a3: (1 - u_2) * (1 - v_1) * w_1 * z
a5: (1 - u_2) * (1 - v_1) * (1 - w_1) * (1 - z)
a1: u_2 * v_1 * w_1 * z
a4: (1 - u_2) * (1 - v_1) * (1 - w_1) * z
c: a2 * (aa - 1) + a3 + a4 + a5
bb: a1 * aa + a2 + a3 + a4 + a5
E: A + (0, 20 * bb)
k = Circle(A, E)
G, H = Intersect(k, l)
nr = Line(H, G)
d: a3 * (aa - 2) + a4 + a5
B = (-1.3583333333333245, -9.558333333333325)
j = Line(A, B)
F, I = Intersect(k, j)
m = Segment(I, F)
D = (5.1, 2.5666666666666713)
p = Line(D, m)
J = Intersect(p, nr)
L: D + c * (J - D)
N: A + d * (L - A)
t = Vector(A, N)
ps1: sgn(t * v)
u = Vector(A, B)
mr = Line(I, F)
n = Segment(H, G)
q = Line(D, n)
K = Intersect(q, mr)
M: D + c * (K - D)
O: A + d * (M - A)
u_1 = Vector(A, O)
ps2: sgn(u * u_1)
w = Vector(A, D)
vw: x(v) * x(w) + y(v) * y(w)
b: ps1 * Distance[A, N] / Distance[A, C]
a: ps2 * Distance[A, O] / Distance[A, B]
uw: x(u) * x(w) + y(u) * y(w)
e: a4 * (aa - 3) + a5
f: a5 * (aa - 4)
r = Segment(L, D)
s = Segment(D, M)
mod_u = Distance(A, B)
T1: a + "\cdot\vec{u}"
T2: b + "\cdot\vec{v}"
T3: "\vec w = " + (LaTeX[a]) + "\cdot\vec{u} + " + (LaTeX[b]) + "\cdot\vec{v}"