π

Acerca

Aleja

-x-2y+3z-6 = 0

π :

x+5y-2z+5 = 0

π ':

Cálculo ángulo entre planos

cos\:α=cos\:\left( \widehat{π,π'}  \right) =cos\:\left( \widehat{\vec{n}_π,\vec{n}_{π'}}  \right) =\frac{\left| \vec{n}_π\:·\vec{n}_{π'} \right| }{\left| \vec{n}_π \right|\:\left|\vec{n}_{π'}  \right|  }=

\vec{n}_π

\vec{n}_{π'}

\vec{n}_{π'}

p': (0 * z) + x + (5 * y) - (2 * z) + 5 = 0
B = PointIn(p')
bz: z(B)
by: y(B)
bx: x(B)
v = OrthogonalVector(p')
c': z(v)
b': y(v)
a': x(v)
g: (a' * bx) + (b' * by) + (c' * bz)
p: (0 * z) + (-x) - (2 * y) + (3 * z) - 6 = 0
A = PointIn(p)
az: z(A)
ay: y(A)
ax: x(A)
u = OrthogonalVector(p)
c: z(u)
b: y(u)
a: x(u)
f: (a * ax) + (b * ay) + (c * az)
O: (0, 0, 0)
d: (-f)
d': (-g)
listapa: {a, b, c, d}
listap'a: {a', b', c', d'}
listap: {a, b, c}
listap': {a', b', c'}
rango2 = MatrixRank({listap, listap'})
rango2a = MatrixRank({listapa, listap'a})
CasillaDeEntrada1 = Textfield(textoplano1)
CasillaDeEntrada2 = Textfield(textoplano2)
textop1: "π:" + (LaTeX[textoplano1]) + ""
textop2: "π':" + (LaTeX[textoplano2]) + ""
r = IntersectPath(p', p)
P = Point(r)
P1: P + u
n1 = Vector(P, P1)
P2: P + v
n2 = Vector(P, P2)
P2' = Mirror(P2, P)
w = Vector(P, P2')
r1 = Line(P, P1)
r2 = Line(P, P2')
α = Angle(r1, r2)
r3 = Line(P, P2)
β = Angle(r1, r3)
r1' = Rotate(r1, 90°, r)
r2' = Rotate(r2, 90°, r)
γ = Angle(r1', r2')
r3' = Rotate(r3, 90°, r)
δ = Angle(r1', r3')
i = false
texto1: "\vec{n}_π=\left(" + (LaTeX[a]) + " ," + (LaTeX[b]) + "," + (LaTeX[c]) + "  \right) "
texto2: "\vec{n}_{π'}=\left(" + (LaTeX[a']) + "," + (LaTeX[b']) + "," + (LaTeX[c']) + "   \right) "
uv: abs((a * a') + (b * b') + (c * c'))
an1: sqrt(a^(2) + b^(2) + c^(2))
texto4 = SurdText(an1)
an2: sqrt(a'^(2) + b'^(2) + c'^(2))
texto6 = SurdText(an2)
texto8: "\left|\vec{n}_π ·\vec{n}_{π'}  \right| =" + (LaTeX[uv]) + ""
cospp': uv / ((an1 * an2))
angpp': (acos(cospp') * 180 / π)
texto10: "α =\:arcos\left( " + (LaTeX[cospp']) + "  \right) =" + (LaTeX[angpp']) + "°"
e: a^(2) + b^(2) + c^(2)
texto5: "\left| \vec{n}_π \right| =\sqrt{" + (LaTeX[e]) + "}"
h: a'^(2) + b'^(2) + c'^(2)
texto7: "\left| \vec{n}_{π'} \right| =\sqrt{" + (LaTeX[h]) + "}"
texto9_1: "=\frac{" + (LaTeX[uv]) + "}{\sqrt{" + (LaTeX[e]) + "}\:·\:\sqrt{" + (LaTeX[h]) + "}}=" + (LaTeX[cospp']) + "⇒" + (LaTeX[texto10]) + ""