A

B

C

D

Paralelepípedo

Tetraedro

Comprobar relación volúmenes

Aleja

Acerca

Producto mixto

Vectores

A = (0, 0, 0)
CasillaDeEntrada1 = Textfield(A)
B = (-2, 1, 0)
CasillaDeEntrada2 = Textfield(B)
C = (1, 1, 0)
CasillaDeEntrada3 = Textfield(C)
D = (1, 0, 2)
CasillaDeEntrada4 = Textfield(D)
u = Vector(A, B)
v = Vector(A, C)
w = Vector(A, D)
a = Line(B, v)
b = Line(C, u)
E = Intersect(a, b)
poli1, a_1, c, e, b_1 = Polygon(A, C, E, B)
d, F, G, H, caraACFD, caraCEGF, caraBEGH, caraABHD, caraDFGH, aristaAD_1, aristaCF, aristaEG, aristaBH_1, aristaDF_1, aristaFG, aristaGH, aristaDH = Prism(poli1, D)
poli2, c_1, a_2, b_2 = Polygon(A, B, C)
p1, caraABD, caraBCD_1, caraACD, aristaAD, aristaBD_1, aristaCD_1 = Pyramid(poli2, D)
g = false
h: false
i = Determinant({{x(u), y(u), z(u)}, {x(v), y(v), z(v)}, {x(w), y(w), z(w)}})
u_x: x(u)
u_y: y(u)
u_z: z(u)
v_x: x(v)
v_y: y(v)
v_z: z(v)
w_x: x(w)
w_y: y(w)
w_z: z(w)
texto1: "\left|\begin{array}{} " + (LaTeX[u_x]) + " & " + (LaTeX[u_y]) + " & " + (LaTeX[u_z]) + " \\ " + (LaTeX[v_x]) + " & " + (LaTeX[v_y]) + " & " + (LaTeX[v_z]) + " \\ " + (LaTeX[w_x]) + " & " + (LaTeX[w_y]) + " & " + (LaTeX[w_z]) + " \\ \end{array}  \right| "
j: abs(i)
k: j / 6
I = Midpoint(A, G)
f' = Mirror(p1, I)
poli3, f_1, d_1, h_1 = Polygon(D, H, F)
p2, caraBDH, caraBFH, caraBDF_1, aristaBD_2, aristaBH, aristaBF = Pyramid(poli3, B)
poli4, c_2, f_2, b_3 = Polygon(F, B, C)
p3, caraBDF, caraBCD, caraCDF, aristaDF, aristaBD, aristaCD = Pyramid(poli4, D)
n = false
J = Midpoint(B, D)
p = Segment(A, J)
K = Midpoint(B, A)
q = Segment(D, K)
C1 = Intersect(q, p)
I' = Mirror(I, C1)
v1 = Vector(C1, I')
t: 0
p'1 = Translate(p1, Vector[(t * v1)])
C2 = baricentro(D, H, F)
I'_1 = Mirror(I, C2)
v2 = Vector(C2, I'_1)
p'2 = Translate(p2, Vector[(t * v2)])
C3 = baricentro(D, F, C)
I'_2 = Mirror(I, C3)
v3 = Vector(C3, I'_2)
p'3 = Translate(p3, Vector[(t * v3)])
p'1' = Mirror(p'1, I)
p'2' = Mirror(p'2, I)
p'3' = Mirror(p'3, I)
texto2: "\overrightarrow{AB}=\left( " + (LaTeX[u_x]) + "," + (LaTeX[u_y]) + "," + (LaTeX[u_z]) + "  \right) "
texto3: "\overrightarrow{AC}=\left(" + (LaTeX[v_x]) + "," + (LaTeX[v_y]) + "," + (LaTeX[v_z]) + "   \right) "
texto4: "\overrightarrow{AD}=\left( " + (LaTeX[w_x]) + "," + (LaTeX[w_y]) + "," + (LaTeX[w_z]) + "  \right) "
rota = 0 (slider from 0 to 1, step 1)
f = false
l: u ⊗ v
texto6: "V_P=\left|\left [\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{AD} \right ]   \right|=\left| " + (LaTeX[i]) + "  \right| = " + (LaTeX[j]) + "\:  u^3 "
texto5: "\left [\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{AD} \right ] = " + (LaTeX[texto1]) + " =" + (LaTeX[i]) + "  "
texto7: "V_T=\frac{1}{6}\left|\left [\overrightarrow{AB},\overrightarrow{AC},\overrightarrow{AD} \right ]   \right|=\frac{" + (LaTeX[j]) + "}{6}=" + (LaTeX[k]) + "\:u^3"
m = true

Tool: baricentro
Input: A, B, D
Output: C1

J = Midpoint(B, D)
p = Segment(A, J)
K = Midpoint(B, A)
q = Segment(D, K)
C1 = Intersect(q, p)