Ecuación vectorial
do plano

$ \vec i $

$ \vec j $

$ \vec k $

$ \overrightarrow{OA} $

$ \vec v $

x_0

y_0

z_0

a

b

c

$ \vec v $

t

X

a'

b'

c'

$ \vec w $

$ \vec w $

s

X

$ \overrightarrow{AX} $

$ α(A,\vec v,\vec w) $

$ \overrightarrow{OX} $

$ α(A,\vec v,\vec w) $

z_0 = 1.5 (slider from -3 to 3, step 0.1)
Z = (0, 10)
O = (0, 0)
G = Dilate(Z, z_0, O)
Y = (10, 0)
f = Line(O, Y)
y_0 = 0.8 (slider from -3 to 3, step 0.1)
F = Dilate(Y, y_0, O)
g = Line(O, Z)
x_0 = 0.8 (slider from -3 to 3, step 0.1)
X = (-3, -5)
E = Dilate(X, x_0, O)
j_2 = Vector(O, Y)
i = Vector(O, X)
j = Vector(O, Z)
e = Line(O, X)
i_2 = Line(E, f)
k = Line(F, e)
m = Line(G, e)
H = Intersect(i_2, k)
n = Line(H, g)
p = Line(O, H)
q = Line(G, p)
A = Intersect(n, q)
OA = Vector(O, A)
j_1 = Line(F, g)
l = Line(G, f)
J = Intersect(j_1, l)
h = Line(E, g)
K = Intersect(h, m)
a = 2.6 (slider from -3 to 3, step 0.1)
b = 1.2 (slider from -3 to 3, step 0.1)
c = 1.1 (slider from -3 to 3, step 0.1)
E' = Dilate(X, a, O)
G' = Dilate(Z, c, O)
F' = Dilate(Y, b, O)
k_1 = Line(E', f)
l_1 = Line(F', e)
m_1 = Line(E', g)
n_1 = Line(F', g)
p_1 = Line(G', e)
q_1 = Line(G', f)
B_1 = Intersect(m_1, p_1)
C_1 = Intersect(k_1, l_1)
D = Intersect(n_1, q_1)
r_1 = Line(B_1, f)
s_1 = Line(D, e)
B = Intersect(r_1, s_1)
OB = Vector(O, B)
texto5: "$ \overrightarrow{OA}=(" + (LaTeX[x_0]) + "," + (LaTeX[y_0]) + "," + (LaTeX[z_0]) + ")$"
A' = Translate(A, OB)
v = Vector(A, A')
t = 2 (slider from -5 to 5, step 0.1)
A'' = Dilate(A', t, A)
tv = Vector(A, A'')
d = Segment(B, A')
vector: "$ \vec u = (" + (LaTeX[a]) + "," + (LaTeX[b]) + "," + (LaTeX[c]) + ") $"
polígono1, o, a_1, a'_1, b_1 = Polygon(O, A, A', B)
a' = 2.6 (slider from -3 to 3, step 0.1)
b' = 2 (slider from -3 to 3, step 0.1)
c' = 1.6 (slider from -3 to 3, step 0.1)
X' = Dilate(X, a', O)
Y' = Dilate(Y, b', O)
Z' = Dilate(Z, c', O)
s_2 = Line(X', f)
d_1 = Line(Y', e)
I = Intersect(s_2, d_1)
e_1 = Line(I, g)
f_1 = Line(O, I)
g_1 = Line(Z', f_1)
C = Intersect(e_1, g_1)
OC = Vector(O, C)
A'_1 = Translate(A, OC)
w = Vector(A, A'_1)
polígono2, o_1, a_3, a'_2, c_2 = Polygon(O, A, A'_1, C)
s = 1.3 (slider from -3 to 3, step 0.1)
L = Dilate(A'_1, s, A)
sw = Vector(A, L)
h_1 = Line(A'', sw)
i_1 = Line(L, tv)
X_2 = Intersect(h_1, i_1)
AX = Vector(A, X_2)
Planoα, a_4, l_2, m_2, a'' = Polygon(A, L, X_2, A'')
OX = Vector(O, X_2)
vector_1: "$ \vec w=(" + (LaTeX[a']) + "," + (LaTeX[b']) + "," + (LaTeX[c']) + ") $"
texto12: "$ \overrightarrow{OX} =(" + (LaTeX[x_0]) + "," + (LaTeX[y_0]) + "," + (LaTeX[z_0]) + ")+" + (LaTeX[t]) + "·(" + (LaTeX[a]) + "," + (LaTeX[b]) + "," + (LaTeX[c]) + ")+" + (LaTeX[s]) + "·(" + (LaTeX[a']) + "," + (LaTeX[b']) + "," + (LaTeX[c']) + ")=(" + (LaTeX[x_0 + t * a + s * a']) + "," + (LaTeX[y_0 + t * b + s * b']) + "," + (LaTeX[z_0 + t * c + s * c']) + ") $"