W

1

2

Aleja

Acerca

a=

b=

-

+

-

+

u=

v=

\vec{w}=a\:\vec{u} +\:b\:\vec{v}

\vec{v}

\vec{u}

Combinación lineal de dos vectores

U

V

u=

v=

\vec{w}=a\:\vec{v_1}+b\:\vec{v_2}⇒

{

{

Sistema
 incompatible.

1

2

Combinación lineal de dos vectores

Expresar un vector como combinación
lineal de otros dos vectores

Expresar un vector como combinación
lineal de otros dos vectores

Cálculo vector w

\vec{w}=a\:\vec{u}+b\:\vec{v}

Solución gráfica

w=

\vec{w}=

\vec{u}=

\vec{v}=

\vec{v}

\vec{u}

\vec{u}=

\vec{v}=

\vec{w}

J: (-2, 2)
a = 2 (slider from -5 to 5, step 0.1)
CasillaDeEntrada1 = Textfield(a)
O = (0, 0)
A: (-2, 2)
u = Vector(O, A)
B: (3, -1)
v = Vector(O, B)
b = 1.5 (slider from -5 to 5, step 0.05)
CasillaDeEntrada2 = Textfield(b)
f = Line(O, A)
g = Line(O, B)
C: O + (a * u)
D: O + (b * v)
t = 0 (slider from 0 to 3, step 0.01)
t1 = If(t < 1, t, 1)
A': O + ((C - O) * t1)
au = Vector(O, A')
B': O + ((D - O) * t1)
bv = Vector(O, B')
h = Line(C, g)
i = Line(D, f)
E = Intersect(h, i)
t3 = If(t ≤ 2, 0, 2 < t ≤ 3, t - 2)
E': O + ((E - O) * t3)
w = Vector(O, E')
CasillaDeEntrada3 = Textfield(A)
CasillaDeEntrada4 = Textfield(B)
ux: x(u)
uy: y(u)
vx: x(v)
vy: y(v)
texto3 = If(b < 0, "", b ≥ 0, "+")
wx: x(w)
wy: y(w)
t2 = If(t ≤ 1, 0, 1 < t ≤ 2, t - 1, t > 2, 1)
F: D + ((E - D) * t2)
G: C + ((E - C) * t2)
j = Segment(D, F)
k = Segment(C, G)
u1: x(J)
u2: y(J)
texto6: "" + (LaTeX[a]) + "\:\vec{u}"
texto7: "" + (LaTeX[b]) + "\:\vec{v}"
ejer: 1
c = Vector((u1, u2))
V1: (5, 1)
V2: (3, 3)
d = Vector(V1)
e = Vector(V2)
CasillaDeEntrada5 = Textfield(V1)
CasillaDeEntrada6 = Textfield(V2)
O' = (0, 0)
U: (u1, u2)
v1x: x(V1)
v1y: y(V1)
v2x: x(V2)
texto11: "" + (LaTeX[u1]) + "=a\left(  " + (LaTeX[v1x]) + " \right) +b\left( " + (LaTeX[v2x]) + " \right) "
v2y: y(V2)
texto12: "" + (LaTeX[u2]) + "=a\:\left( " + (LaTeX[v1y]) + "  \right) +b\:\left(" + (LaTeX[v2y]) + "   \right) "
as: ((u1 * v2y) - (v2x * u2)) / ((v1x * v2y) - (v2x * v1y))
texto15 = SurdText(as)
r1 = Line(V2, O')
H: (as * V1)
m = Line(H, r1)
bs: ((v1x * u2) - (v1y * u1)) / ((v1x * v2y) - (v2x * v1y))
texto16 = SurdText(bs)
n: (as * d) + (bs * e)
r2 = Line(O', V1)
sol2_1 = AreParallel(r1, r2)
q = Line(U, d)
I: (bs * V2)
texto2: "\vec{w}=" + (LaTeX[a]) + "\left(" + (LaTeX[ux]) + "  ," + (LaTeX[uy]) + " \right) " + (LaTeX[texto3]) + "" + (LaTeX[b]) + "\left(" + (LaTeX[vx]) + "," + (LaTeX[vy]) + "   \right)  =" + (LaTeX[G]) + ""
texto8: "\vec{w}=" + (LaTeX[a]) + "\:\vec{u}" + (LaTeX[texto3]) + "" + (LaTeX[b]) + "\:\vec{v}"
o = false
texto23: "\vec{w}=" + (LaTeX[U]) + ""
s = 0 (slider from 0 to 2.1, step 0.05)
s1 = If(s ≤ 1, s, 1)
K: O' + ((H - O') * s1)
l = Vector(K)
L: O' + ((I - O') * s1)
p = Vector(L)
s2 = If(s ≤ 1, 0, 1 < s ≤ 2, s - 1, 2 < s < 3, 1)
M: H + ((U - H) * s2)
f_1 = Segment(H, M)
N: I + ((U - I) * s2)
r = Segment(I, N)
texto24: "" + (LaTeX[texto15]) + "\vec{u}"
texto25: "" + (LaTeX[texto16]) + "\vec{v}"
P = (-0.394, -1.71)
Q = (0.026, -1.71)
texto27 = If(bs < 0, "", bs > 0, "+")
texto26: "" + (LaTeX[texto15]) + "\vec{u}" + (LaTeX[texto27]) + "" + (LaTeX[texto16]) + "\vec{v}"
sol2 = false
CasillaDeEntrada7 = Textfield(J)
texto28: "" + (LaTeX[J]) + "=a" + (LaTeX[V1]) + "+b" + (LaTeX[V2]) + ""
texto37: "\begin{cases}" + (LaTeX[texto11]) + " \\" + (LaTeX[texto12]) + " \end{cases}"
texto17: "Sol:a=" + (LaTeX[texto15]) + ", b=" + (LaTeX[texto16]) + ""