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P

Q

Q'=

r:

Cálculo d(P,r)

Interpretación geométrica

\overrightarrow{QP}

\vec{u}_r

Q = (3, -2, 0.9999999999999982)
Q' = (0, -1, 3.0000000000000018)
P = (3, -2, -2)
CasillaDeEntrada1 = Textfield(P)
CasillaDeEntrada2 = Textfield(Q)
CasillaDeEntrada3 = Textfield(Q')
O = Intersect(xAxis, yAxis)
u = Vector(Q, Q')
r = Line(Q, u)
qp = Vector(Q, P)
w: u ⊗ qp
u1: x(u)
u2: y(u)
u3: z(u)
qp1: x(qp)
qp2: y(qp)
qp3: z(qp)
w1: x(w)
w2: y(w)
w3: z(w)
aw: abs(w)
av: abs(qp)
au: abs(u)
aw2: w1^(2) + w2^(2) + w3^(2)
au2: u1^(2) + u2^(2) + u3^(2)
texto8: "\left| \vec{u}_r \right| =\sqrt{" + (LaTeX[au2]) + "}"
dpr: aw / au
g = OrthogonalLine(P, r, space)
P_r = Intersect(r, g)
h = Segment(P_r, P)
α = Angle(Q, P_r, P)
texto11: "d = " + dpr + " "
A: Q + u
u_1 = Vector(Q, A)
i = false
j = Line(A, qp)
k = Line(P, r)
B = Intersect(k, j)
polígono1, a, q, p_1, b = Polygon(A, Q, P, B)
i1: false
C: Q + w
wq = Vector(Q, C)
texto12: "\left|\vec{u}_r×\overrightarrow{QP}  \right| =\sqrt{" + (LaTeX[aw2]) + "}"
texto13: "r:\:" + (LaTeX[Q]) + "\:+λ\left(" + (LaTeX[u1]) + "," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "   \right) "
F: Q + u
texto6: "\vec{u}_r\:×\overrightarrow{QP}=\left| \begin{array}{} i & j & k \\ " + (LaTeX[u1]) + " & " + (LaTeX[u2]) + " & " + (LaTeX[u3]) + "\\  " + (LaTeX[qp1]) + "& " + (LaTeX[qp2]) + " & " + (LaTeX[qp3]) + " \\ \end{array} \right| =\left(" + (LaTeX[w1]) + " ," + (LaTeX[w2]) + "," + (LaTeX[w3]) + "  \right) "
texto7: "\left| \vec{u}_r×\overrightarrow{QP\:} \right| =\sqrt{" + (LaTeX[aw2]) + "}"
texto9: "d(P,r)=\frac{\left| \vec{u}_r×\overrightarrow{QP\:} \right| }{\left| \vec{u}_r \right| }=\frac{\sqrt{" + (LaTeX[aw2]) + "}}{\sqrt{" + (LaTeX[au2]) + "}}=" + (LaTeX[dpr]) + "\:u"
texto1: "\overrightarrow{QP}=\left(" + (LaTeX[qp1]) + "," + (LaTeX[qp2]) + "," + (LaTeX[qp3]) + "   \right) "
texto2: "\vec{u}_r=\left(" + (LaTeX[u1]) + "," + (LaTeX[u2]) + "," + (LaTeX[u3]) + "   \right) "