Acerca

Aleja

-2x+3y +z -4= 0

π :

A

B

r :

sen\:α=cos\left(90°-α   \right) =\frac{\left|\vec{u}·\vec{n}_π  \right| }{\left|\vec{u}  \right| \left| \vec{n}_π \right| }

Ángulo entre recta y plano

\vec{n}_π

\vec{n}_π

\vec{u}

\vec{u}=\overrightarrow{AB}

A: (4, -3, -1)
B = (0, -2, 2)
f = Line(A, B)
u = Vector(A, B)
p: (0 * z) + (-2 * x) + (3 * y) + z - 4 = 0
a1: x(A)
a2: y(A)
a3: z(A)
u1: x(u)
u2: y(u)
u3: z(u)
C = PointIn(p)
n = OrthogonalVector(p)
d: (x(C) * x(n)) + (y(C) * y(n)) + (z(C) * z(n))
a: x(n)
b: y(n)
c: z(n)
CasillaDeEntrada1 = Textfield(texto0)
CasillaDeEntrada2 = Textfield(A)
CasillaDeEntrada3 = Textfield(B)
texto11: "r:" + f + ""
O: (0, 0, 0)
P = Intersect(f, p)
i: false
α = Angle(f, p)
texto1: "\vec{n}_π=\left(" + (LaTeX[a]) + " ," + (LaTeX[b]) + "," + (LaTeX[c]) + "  \right) "
D: P + n
w = Vector(P, D)
e = Plane(A, B, D)
g = IntersectPath(e, p)
k = false
an: abs(n)
au: abs(u)
texto6 = SurdText(au)
texto7: "\left| \vec{u} \right| =" + (LaTeX[texto6]) + ""
aun: abs((u * n))
texto4 = SurdText(an)
texto3: "\left| \vec{n}_π \right| =" + (LaTeX[texto4]) + ""
texto8: "\left| \vec{u}·\vec{n}_π \right| =" + (LaTeX[aun]) + ""
senang: aun / ((an * au))
texto9: "sen\:α=sen\left( \widehat{r,π}  \right) =\frac{" + (LaTeX[aun]) + "}{" + (LaTeX[texto6]) + "·" + (LaTeX[texto4]) + "}=" + (LaTeX[senang]) + ""
ang: (asin(senang) * 180 / π)
texto10: "α=arcsen\left(" + (LaTeX[senang]) + "   \right) =" + (LaTeX[ang]) + "°"
D' = Mirror(D, P)
v = Vector(P, D')
l = Line(D, D')
β = Angle(f, l)
γ = Angle(l, g)
m = Line(D', D)
δ = Angle(m, f)
B' = Translate(B, Vector[A, P])
q = Vector(P, B')
texto5: "\vec{u}=\overrightarrow{AB}=\left(" + (LaTeX[u1]) + " ," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "  \right) "
texto16: "π:" + (LaTeX[texto0]) + ""
texto17: "r:\left(" + (LaTeX[a1]) + " ," + (LaTeX[a2]) + "," + (LaTeX[a3]) + "  \right) +λ\left( " + (LaTeX[u1]) + "," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "  \right) "
texto12: "\vec{u}=\left(" + (LaTeX[u1]) + " ," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "  \right) "