Acerca

Aleja

r : P

s : Q

Q'

r:

P'

s:

Cálculo perpendicular común t

\vec{v}

\vec{v}

v

π

π '

Perpendicular común

Hay infinitas rectas solución.

A

\vec{u}_r

\vec{u}_s

Q: (1, -3, 0)
Q' = (0, -1, 1)
P: (-2, -2, 1)
CasillaDeEntrada1 = Textfield(P)
CasillaDeEntrada2 = Textfield(Q)
CasillaDeEntrada3 = Textfield(Q')
O = Intersect(xAxis, yAxis)
u_s = Vector(Q, Q')
s = Line(Q, u_s)
qp = Vector(Q, P)
u'1: x(u_s)
u'2: y(u_s)
u'3: z(u_s)
qp1: x(qp)
qp2: y(qp)
qp3: z(qp)
P': (-1, -1, 2)
CasillaDeEntrada4 = Textfield(P')
u_r = Vector(P, P')
r = Line(P, u_r)
listau: {u'1, u'2, u'3}
listaqp: {qp1, qp2, qp3}
listav: {x(u_r), y(u_r), z(u_r)}
ran2 = MatrixRank({listau, listav})
ran3 = MatrixRank({listau, listav, listaqp})
texto5 = If(ran2 ≟ 1 ∧ ran3 ≟ 1, "Las rectas r y s son coincidentes", ran2 ≟ 1 ∧ ran3 ≟ 2, "Las rectas r y s son paralelas", ran2 ≟ 2 ∧ ran3 ≟ 2, "Las rectas r y s son secantes", ran2 ≟ 2 ∧ ran3 ≟ 3, "Las rectas r y s se cruzan")
v_1: u_r ⊗ u_s
E: P + v_1
v = Vector(P, E)
G: Q + v
p' = Plane(Q, Q', G)
p = Plane(P, E, P')
t = IntersectPath(p', p)
I = Intersect(s, t)
J = Intersect(r, t)
t_1 = Segment(I, J)
i = false
u1: x(u_r)
u2: y(u_r)
u3: z(u_r)
texto1: "r:" + (LaTeX[P]) + "+λ\left( " + (LaTeX[u1]) + "," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "  \right) "
texto2: "s:" + (LaTeX[Q]) + "+λ\left( " + (LaTeX[u'1]) + "," + (LaTeX[u'2]) + "," + (LaTeX[u'3]) + "  \right) "
v1: x(v)
v2: y(v)
v3: z(v)
texto11 = If(x(P) < 0, ("x+" * abs(x(P))), x(P) ≟ 0, "x", x(P) > 0, ("x-" * abs(x(P))))
texto12 = If(y(P) < 0, ("y+" * abs(y(P))), y(P) ≟ 0, "y", y(P) > 0, ("y-" * abs(y(P))))
texto13 = If(z(P) < 0, ("z+" * abs(z(P))), z(P) ≟ 0, "z", z(P) > 0, ("z-" * abs(z(P))))
texto14: "π:\left| \begin{array}{} " + (LaTeX[texto11]) + " & " + (LaTeX[texto12]) + " & " + (LaTeX[texto13]) + " \\ " + (LaTeX[u1]) + " & " + (LaTeX[u2]) + " & " + (LaTeX[u3]) + " \\ " + (LaTeX[v1]) + " & " + (LaTeX[v2]) + " & " + (LaTeX[v3]) + "\\ \end{array} \right| =0⇒π:" + (LaTeX[p]) + ""
texto21 = If(x(Q) < 0, ("x+" * abs(x(Q))), x(Q) ≟ 0, "x", x(Q) > 0, ("x-" * abs(x(Q))))
texto22 = If(y(Q) < 0, ("y+" * abs(y(Q))), y(Q) ≟ 0, "y", y(Q) > 0, ("y-" * abs(y(Q))))
texto23 = If(z(Q) < 0, ("z+" * abs(z(Q))), z(Q) ≟ 0, "z", z(Q) > 0, ("z-" * abs(z(Q))))
texto24: "π':\left| \begin{array}{} " + (LaTeX[texto21]) + " & " + (LaTeX[texto22]) + " & " + (LaTeX[texto23]) + " \\ " + (LaTeX[u'1]) + " & " + (LaTeX[u'2]) + " & " + (LaTeX[u'3]) + "\\ " + (LaTeX[v1]) + " & " + (LaTeX[v2]) + " & " + (LaTeX[v3]) + " \\ \end{array} \right|=0⇒π':" + (LaTeX[p']) + " "
A: Q + v
u = Vector(Q, A)
i1: false
i2: false
i3: false
i4: false
texto10: "t:\begin{cases} " + (LaTeX[p]) + "  \\  " + (LaTeX[p']) + " \end{cases}"
B = Point(r)
f = OrthogonalLine(B, s, space)
texto15: "\vec{u}_r=\left(  " + (LaTeX[u1]) + "," + (LaTeX[u2]) + "," + (LaTeX[u3]) + " \right) "
texto16: "\vec{u}_s=\left( " + (LaTeX[u'1]) + "," + (LaTeX[u'2]) + "," + (LaTeX[u'3]) + "  \right) "
texto6: "\vec{v}=\vec{u}_r×\vec{u}_s=\left| \begin{array}{} i & j & k \\ " + (LaTeX[u1]) + " & " + (LaTeX[u2]) + " & " + (LaTeX[u3]) + "\\ " + (LaTeX[u'1]) + " & " + (LaTeX[u'2]) + "& " + (LaTeX[u'3]) + "\\ \end{array} \right| =\left( " + (LaTeX[v1]) + "," + (LaTeX[v2]) + "," + (LaTeX[v3]) + "  \right) "