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\left.\ \begin{array}{} x=a_1+λu_1 \ y=a_2+λu_2 \ z=a_3+λu_3 \end{array}  \right\} 

No tiene solución⇒ Recta paralela a plano.

Infinitas soluciones ⇒ Recta contenida en plano

Solución única⇒ Recta corta al plano.

2x+y +2z  -2= 0

p:

A

B

Sustituyendo x, y, z en la ecuación del plano p:

Plano paralelo a P por A

Punto de intersección

Cálculo algebraico

r :

A = (-3, 2, 0)
B = (-2, 0, 2)
f = Line(A, B)
u = Vector(A, B)
p: (0 * z) + (2 * x) + y + (2 * z) - 2 = 0
a1: x(A)
a2: y(A)
a3: z(A)
u1: x(u)
u2: y(u)
u3: z(u)
texto2: "\left.\ \begin{array}{} x=" + (LaTeX[a1]) + "+λ(" + (LaTeX[u1]) + ") \\ y=" + (LaTeX[a2]) + "+λ(" + (LaTeX[u2]) + ") \\ z=" + (LaTeX[a3]) + "+λ(" + (LaTeX[u3]) + ") \end{array}  \right\} "
C = PointIn(p)
v = OrthogonalVector(p)
d: (x(C) * x(v)) + (y(C) * y(v)) + (z(C) * z(v))
a: x(v)
b: y(v)
c: z(v)
texto3: "" + (LaTeX[p]) + ""
texto4: "" + (LaTeX[a]) + "(" + (LaTeX[a1]) + "+λ(" + (LaTeX[u1]) + "))+" + (LaTeX[b]) + "(" + (LaTeX[a2]) + "+λ(" + (LaTeX[u2]) + "))+" + (LaTeX[c]) + "(" + (LaTeX[a3]) + "+λ(" + (LaTeX[u3]) + "))=" + (LaTeX[d]) + ""
e: (a * a1) + (b * a2) + (c * a3)
num: d - e
den: (a * u1) + (b * u2) + (c * u3)
texto6: "" + (LaTeX[den]) + " ·λ=" + (LaTeX[num]) + ""
sol: num / den
dentro: num ≟ 0 ∧ den ≟ 0
paral: num ≠ 0 ∧ den ≟ 0
corta: den ≠ 0
CasillaDeEntrada1 = Textfield(texto0)
CasillaDeEntrada2 = Textfield(A)
CasillaDeEntrada3 = Textfield(B)
texto11: "r:" + f + ""
texto12: "\vec{u}=\overrightarrow{AB}=\left(" + (LaTeX[u1]) + " ," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "  \right) "
O: (0, 0, 0)
g = false
h = Plane(A, p)
P = Intersect(f, p)
i: false
texto14: "P" + P + ""
j: num / den
texto5: "λ=\frac{" + (LaTeX[num]) + "}{" + (LaTeX[den]) + "}=" + (LaTeX[j]) + ""
k = false
dA: (x(A) * x(v)) + (y(A) * y(v)) + (z(A) * z(v))
aplano: dA ≟ d
texto10_1: "" + (LaTeX[e]) + "+ λ(" + (LaTeX[den]) + ")=" + (LaTeX[d]) + ""