Acerca

Aleja

A

B

A'

B'

Posición rectas y cálculo de ángulo

r :

s :

\vec{u}

\vec{v}

A: (-1, -1, -1)
B: (2, 2, 2)
O: (0, 0, 0)
u = Vector(A, B)
A': (2, 4, -1)
CasillaDeEntrada1 = Textfield(A)
CasillaDeEntrada2 = Textfield(B)
r = Line(A, B)
CasillaDeEntrada3 = Textfield(A')
B': (0, -2, 3)
v = Vector(A', B')
s = Line(A', B')
CasillaDeEntrada4 = Textfield(B')
uv: (u * v)
auv: abs(uv)
au: abs(u)
av: abs(v)
cosuv: auv / ((au * av))
acosuv: acos(cosuv)
ang: (acosuv * 180 / π)
u1: x(u)
u2: y(u)
u3: z(u)
texto1 = SurdText(au)
texto2: "\left| \vec{u} \right| =" + (LaTeX[texto1]) + ""
texto3 = SurdText(av)
texto4: "\left|\vec{v }\right| =" + (LaTeX[texto3]) + ""
texto5: "\vec{u}\:·\:\vec{v}=" + (LaTeX[uv]) + ""
texto6: "\left| \vec{u}\:·\:\vec{v} \right| =" + (LaTeX[auv]) + ""
texto8 = SurdText(cosuv)
texto10: "r:" + (LaTeX[A]) + "+λ\left(" + (LaTeX[u1]) + "," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "   \right) "
v1: x(v)
v2: y(v)
v3: z(v)
texto11: "s:" + (LaTeX[A']) + "+λ\left( " + (LaTeX[v1]) + " ," + (LaTeX[v2]) + "," + (LaTeX[v3]) + " \right) "
w = Vector(A, A')
ranuv = MatrixRank({{x(u), y(u), z(u)}, {x(v), y(v), z(v)}})
w1: x(w)
w2: y(w)
w3: z(w)
ranuvw = MatrixRank({{x(u), y(u), z(u)}, {x(v), y(v), z(v)}, {x(w), y(w), z(w)}})
cruzan: ranuv ≟ 2 ∧ ranuvw ≟ 3
texto12 = If(ranuv ≟ 2 ∧ ranuvw ≟ 3, "Las rectas r y s se cruzan", ranuv ≟ 2 ∧ ranuvw ≟ 2, "Las rectas r y s se cortan", ranuv ≟ 1 ∧ ranuvw ≟ 2, "Las rectas r y s con paralelas", ranuv ≟ 1 ∧ ranuvw ≟ 1, "Las rectas r y s son coincidentes")
f: z = 0
s' = Translate(s, Vector[(-w)])
texto9: "\vec{u}=\left( " + (LaTeX[u1]) + "," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "  \right) "
texto13: "\vec{v}=\left(" + (LaTeX[v1]) + " ," + (LaTeX[v2]) + "," + (LaTeX[v3]) + "  \right) "
i: false
α = Angle(r, s)
g = Line(B', A')
β = Angle(r, g)
texto14: "α=arccos\left(  " + (LaTeX[cosuv]) + " \right) =" + (LaTeX[ang]) + "°"
γ = Angle(r, s')
h = Line(B, A)
δ = Angle(h, s')
texto7: "cos\:α=cos\left(\widehat{r,s}   \right) =\frac{" + (LaTeX[auv]) + "}{" + (LaTeX[texto1]) + "\:·\:" + (LaTeX[texto3]) + "}=" + (LaTeX[cosuv]) + ""
a = false