A=

B=

D=

a x + b y + c z + d=0

Plano paralelo

Haz de planos paralelos

C=

Plano del haz por punto P

1

2

1

2

A'=

B'=

C'=

D'=

a 'x+b \; 'y+c \; 'z+d \; '=0

Ver haz

(a \; x+b \; y+c \; z \; +d)+\lambda(a'x+b'y+c'z+d')=0

P

Acerca

Aleja

Los plano no son secantes.

a = -1 (slider from -5 to 5, step 0.05)
b = -1 (slider from -5 to 5, step 0.05)
c = -3 (slider from -5 to 5, step 0.05)
d = 4 (slider from -5 to 5, step 0.05)
A = Textfield(a)
CasillaDeEntrada2 = Textfield(b)
CasillaDeEntrada4 = Textfield(d)
s = -11 (slider from -20 to 20, step 1)
pp: (a * x) + (b * y) + (c * z) + d + s = 0
p1: (a * x) + (b * y) + (c * z) + d = 0
g = false
h = false
CasillaDeEntrada3 = Textfield(c)
P = (3, 1, 4)
pA = Plane(P, p1)
f: false
texto4: "" + (LaTeX[pA]) + ""
e: d + s
haz: 1
texto8 = If(haz ≟ 1, "Haz de planos paralelos", "Haz de planos secantes")
a': 1
b': 1
c': 1
d' = -1
A' = Textfield(a')
CasillaDeEntrada6 = Textfield(b')
CasillaDeEntrada7 = Textfield(c')
CasillaDeEntrada8 = Textfield(d')
p2: (a' * x) + (b' * y) + (c' * z) + d' = 0
r2 = IntersectPath(p2, p1)
landa = 3 (slider from -40 to 40, step 1)
k: (a * x) + (b * y) + (c * z) + d + (landa * ((a' * x) + (b' * y) + (c' * z) + d')) = 0
texto6: "" + (LaTeX[k]) + ""
p21(x, y, z) = (a * x) + (b * y) + (c * z) + d
p12(x, y, z) = (a * x) + (b * y) + (c * z) + e
texto3: "" + (LaTeX[p12]) + "=0"
n = false
p22(x, y, z) = (a' * x) + (b' * y) + (c' * z) + d'
p = 12 (slider from 1 to 20, step 1)
inc = If(p ≟ 1, 1, p ≟ 2, 2, p ≟ 3, 3, p ≟ 4, 4, p ≟ 5, 5, p ≟ 6, 6, p ≟ 7, 8, p ≟ 8, 10, p ≟ 9, 12, p ≟ 10, 15, p ≟ 11, 18, p ≟ 12, 20)
p22s = Simplify(p22)
p21s = Simplify(p21)
texto11: "\left(" + (LaTeX[p21s]) + "   \right) +\lambda\left(" + (LaTeX[p22s]) + "   \right) =0"
i = false
lista2 = Sequence(Rotate[p2, ((i * inc))°, r2], i, 1, 360 / inc)
texto12: "λ=" + landa + ""
ax: x(P)
ay: y(P)
az: z(P)
CasillaDeEntrada9 = Textfield(P)
sep = 0.75 (slider from 0.25 to 2, step 0.25)
num = 8 (slider from 5 to 20, step 1)
u = OrthogonalVector(p1)
v = UnitVector(u)
lista1 = Sequence(Translate[p1, Vector[((sep * i) * v)]], i, (-num), num)
texto5: "D'=" + (LaTeX[e]) + ""
aa': a / a'
bb': b / b'
cc': c / c'
dd': d / d'
ab: aa' ≟ bb'
ac: aa' ≟ cc'
abc: ab ∧ ac
texto2: "π:" + (LaTeX[p21s]) + "=0"
texto9: "π':" + (LaTeX[p22s]) + "=0"