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Aleja

-x - y + 6z - 20 = 0

π :

-x  - y + 6z +14 = 0

π ':

1

2

Distancia de un punto a un plano

Distancia entre dos planos

P

Cálculo d(P, π )

1

2

d(π,π')=0

P

p': (0 * z) + (-x) - y + (6 * z) + 14 = 0
v = OrthogonalVector(p')
a': x(v)
b': y(v)
c': z(v)
B = PointIn(p')
bx: x(B)
by: y(B)
bz: z(B)
g: (a' * bx) + (b' * by) + (c' * bz)
d': (-g)
p: (0 * z) + (-x) - y + (6 * z) - 20 = 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)
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]) + ""
caso: 1
P = (2, 8, -2)
CasillaDeEntrada3 = Textfield(P)
r = OrthogonalLine(P, p)
P' = Intersect(r, p)
p1: x(P)
p2: y(P)
p3: z(P)
num1: abs((a * p1) + (b * p2) + (c * p3) + d)
den11: a^(2) + b^(2) + c^(2)
dispp1: num1 / sqrt(den11)
i = Segment(P, P')
texto3: "d(P,π)=" + dispp1 + ""
j = false
texto5: "d(P,π)=\frac{\left| " + (LaTeX[a]) + "\left( " + (LaTeX[p1]) + "  \right) +\left( " + (LaTeX[b]) + "  \right)\left( " + (LaTeX[p2]) + "  \right) +\left( " + (LaTeX[c]) + "  \right) \left( " + (LaTeX[p3]) + "  \right)+\left( " + (LaTeX[d]) + "  \right)    \right| }{\sqrt{\left( " + (LaTeX[a]) + "  \right)^2+\left( " + (LaTeX[b]) + "  \right)^2+\left(  " + (LaTeX[c]) + " \right) ^2  }}="
texto1': "" + texto1 + ""
texto2': "" + texto2 + ""
texto4: "\frac{" + (LaTeX[a]) + "}{" + (LaTeX[a']) + "}"
texto7: "\frac{" + (LaTeX[b]) + "}{" + (LaTeX[b']) + "}"
texto8: "\frac{" + (LaTeX[c]) + "}{" + (LaTeX[c']) + "}"
texto9: "\frac{" + (LaTeX[d]) + "}{" + (LaTeX[d']) + "}"
aa': a / a'
bb': b / b'
cc': c / c'
texto11 = If(b / b' ≟ c / c', "=", "≠")
dd': d / d'
texto10 = If(a / a' ≟ b / b', "=", "≠")
texto12 = If(c / c' ≟ d / d', "=", "≠")
lista1: listap / listap'
lista2 = Unique(lista1)
texto13 = If(rango2 ≟ 2, " Los planos  π  y  π ' son secantes", rango2 ≟ 1 ∧ rango2a ≟ 2, "Los planos  π  y  π ' son paralelos", rango2a ≟ 1, "Los planos  π y  π ' son coincidentes")
P'' = PointIn(p)
h = OrthogonalLine(P'', p)
num2: abs((x(P'') * a') + (y(P'') * b') + (z(P'') * c') + d')
dispp2: num2 / sqrt(den11)
texto16: "π: " + p + ""
texto17: "π: " + p' + ""
C = Intersect(h, p')
k = Segment(P'', C)
texto6: "=\frac{" + (LaTeX[num1]) + "}{\sqrt{" + (LaTeX[den11]) + "}}= " + (LaTeX[dispp1]) + "\:u"
texto19: "π:" + (LaTeX[textoplano1]) + ""
texto20: "π':" + textoplano2 + ""
den12: a'^(2) + b'^(2) + c'^(2)
dis2: num2 / sqrt(den12)
texto15: "d\left(π,π'   \right)=d\left(P,π' \right) =\frac{" + (LaTeX[num2]) + "}{\sqrt{" + (LaTeX[den12]) + "}}=" + (LaTeX[dis2]) + "\:u"
texto18: "d=" + dis2 + ""
texto21: "P" + (LaTeX[P'']) + "\:∈π"