Acerca

Aleja

=

=

A(x-a_1)+B(y-a_2)+C(z-a_3)=0

X(x,y,z)

P(a_1,a_2,a_3)

\vec{n}=(A,B,C)

Sustituyendo valores y operando
se obtiene la ecuación del plano.

Ecuación normal del plano

\vec{n}⊥\overrightarrow{PX}⇔\vec{n}\:·\overrightarrow{PX}\:=\:0

\vec{n}

\overrightarrow{PX}

\vec{n}

P = (-1, -3, 2)
N: (1, 1, 1)
CasillaDeEntrada1 = Textfield(P)
n = Vector((0, 0, 0), N)
a = OrthogonalPlane(P, n)
Q: P + n
u = Vector(P, Q)
CasillaDeEntrada2 = Textfield(N)
a1: x(P)
a2: y(P)
a3: z(P)
A: x(n)
B: y(n)
C: z(n)
X = PointIn(a)
v = Vector(P, X)
D: (-((A * a1) + (B * a2) + (C * a3)))
aa: abs(A)
ab: abs(B)
ac: abs(C)
ad: abs(D)
texto2 = If(A < -1, (("-" * aa) * "x"), A ≟ -1, "-x", -1 < A < 0, (("-" * aa) * "x"), A ≟ 0, "", 0 < A < 1, (("" * aa) * "x"), A ≟ 1, "x", A > 1, (("" * aa) * "x"))
texto3 = If(B < -1, (("-" * ab) * "y"), B ≟ -1, "-y", -1 < B < 0, (("-" * ab) * "y"), B ≟ 0, "", 0 < B < 1, (("+" * ab) * "y"), B ≟ 1, "+y", B > 1, (("+" * ab) * "y"))
texto4 = If(C < -1, (("-" * ac) * "z"), C ≟ -1, "-z", -1 < C < 0, (("-" * ac) * "z"), C ≟ 0, "", 0 < C < 1, (("+" * ac) * "z"), C ≟ 1, "+z", C > 1, (("+" * ac) * "z"))
texto5 = If(D < 0, ("-" * ad), D ≟ 0, "", D > 0, ("+" * ad))
i = true
α = Angle(X, P, Q)
texto14: "" + (LaTeX[a]) + ""
texto6: "π:" + (LaTeX[texto2]) + "" + (LaTeX[texto3]) + "" + (LaTeX[texto4]) + "" + (LaTeX[texto5]) + "=0"