四面體的體積(2)
Author: 藍邦偉  老師

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單位向量

座標軸

\vec{a}=(

\vec{b}=(

\vec{c}=(

p

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p

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p

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a

q

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w

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e

)

b

1

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f

)

c

四面體的體積

r

Reset

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α = 4.014257279586958 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
β = 1.3089969389957472 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O = (10.16740152323446, 3.747511447705269)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
Z_{unit}: O + (0, sin(β))
u = Vector(O, X_{unit})
v = Vector(O, Y_{unit})
w = Vector(O, Z_{unit})
L = NaN (slider from 1 to 7, step 1)
A_1: O + L * u
B_1: O + L * v
Z: O + L * w
c = false
d = true
Q_2: 0.25 * Corner[2] + 0.75 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
多邊形1, e, q_2, q_3, f = Polygon(Corner[1], Q_2, Q_3, Corner[4])
x1 = 0
y1 = 0
z1 = 0
x2 = 0
y2 = 0
z2 = 0
x3 = 0
y3 = 0
z3 = 0
inputBox1 = Textfield(x1)
inputBox2 = Textfield(y1)
inputBox3 = Textfield(z1)
P_1: O + x1 * u + y1 * v + z1 * w
h = Vector(O, P_1)
inputBox4 = Textfield(x2)
inputBox5 = Textfield(y2)
inputBox6 = Textfield(z2)
P_2: O + x2 * u + y2 * v + z2 * w
A = Point(h)
i = Vector(A, P_2)
inputBox7 = Textfield(x3)
inputBox9 = Textfield(z3)
P_3: O + x3 * u + y3 * v + z3 * w
j = Vector(A, P_3)
P_4: P_1 + P_2 - O
P_5: P_2 + P_3 - O
P_6: P_1 + P_3 - O
P_7: P_4 + P_6 - P_1
poly2, g, k, m = Polygon(P_2, P_1, P_3)
l = 5.1 (slider from 1 to 8, step 0.1)
b = Vector(O - l * w, O + l * w)
a = Vector(O - l * v, O + l * v)
z = Vector(O - l * u, O + l * u)
δ: abs(x1 * y2 * z3 + y1 * z2 * x3 + z1 * x2 * y3 - z3 * y2 * x1 - y1 * x2 * z3 - x1 * y3 * z2)
inputBox8 = Textfield(y3)
n = Segment(P_1, P_2)
p = Segment(P_3, P_2)
q = Segment(P_3, P_1)
text14: "V=\frac{1}{6}|\left\vert \begin{array}{} " + (LaTeX[x1]) + " &" + (LaTeX[y1]) + " &" + (LaTeX[z1]) + " \\" + (LaTeX[x2]) + " & " + (LaTeX[y2]) + " &" + (LaTeX[z2]) + " \\" + (LaTeX[x3]) + " &" + (LaTeX[y3]) + " &" + (LaTeX[z3]) + "\\ \end{array} \right\vert| =\frac{" + (LaTeX[δ]) + "}{6}=" + (LaTeX[FractionText[δ / 6]]) + ""