直線的參數式
Author: 藍邦偉  老師

x

y

z

單位向量

座標軸

x

y

z

直線的參數式

a

b

c

x_0

y_0

P點座標

(

,

,

)

方向向量

\overrightarrow{L}=(

,

,

)

z_0

1

2

d = 1 (slider from 0 to 5, step 0.5)
c = 4 (slider from -5 to 5, step 1)
b = 2 (slider from -5 to 5, step 1)
a = 3 (slider from -5 to 5, step 1)
z_0 = 1 (slider from -L + 1 to L - 1, step 1)
y_0 = 1 (slider from -L + 1 to L - 1, step 1)
x_0 = 1 (slider from -L + 1 to L - 1, step 1)
O = (10.116963408585987, 4.121423319306392)
β = 1.5009831567151233 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 4.363323129985824 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
P: O + x_0 * u + y_0 * v + z_0 * w
l = Vector(P, P + a * u + b * v + c * w)
L = 6 (slider from 1 to 10, step 1)
a_1 = Vector(O - L * v, O + L * v)
b_1 = Vector(O - L * w, O + L * w)
z_1 = Vector(O - L * u, O + L * u)
A_1: O + L * u
B_1: O + L * v
Z: O + L * w
c_1 = false
d_2 = 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])
g = Segment(Q_2, Q_3)
h = Line(P, l)
t = 6.75 (slider from 0 to 8, step 0.01)
P_1: P + d * l
P_a: O + x_0 * u
P_b: O + y_0 * v
P_c: O + z_0 * w
P_d: O + x_0 * u + y_0 * v
P_e: O + y_0 * v + z_0 * w
P_f: O + z_0 * w + x_0 * u
z = 1 (slider from 0.1 to 5, step 0.1)
i = Segment(P_f, P_a)
j = Segment(P_f, P_c)
k = Segment(P_c, P_e)
m_1 = Segment(P_e, P_b)
n = Segment(P_b, P_d)
p = Segment(P, P_d)
q = Segment(P_f, P)
r = Segment(P, P_e)
s = Segment(P_a, P_d)
P_G: O
d_1 = Segment(P_c, P_G)
e_1 = Segment(P_a, P_G)
f_1 = Segment(P_G, P_b)
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
inputBox4 = Textfield(x_0)
inputBox5 = Textfield(y_0)
u_1 = Vector(P, P_1)
P_2: P - d * l
v_1 = Vector(P, P_2)
if: i * f
inputBox6 = Textfield(z_0)
text15: "L:\left\lbrace \begin{array}{ll} x=" + (LaTeX[x_0]) + "" + (LaTeX[If[a < 0, "-", "+"]]) + "" + (LaTeX[abs(a)]) + "t\\ y=" + (LaTeX[y_0]) + "" + (LaTeX[If[b < 0, "-", "+"]]) + "" + (LaTeX[abs(b)]) + "t\\ z=" + (LaTeX[z_0]) + "" + (LaTeX[If[c < 0, "-", "+"]]) + "" + (LaTeX[abs(c)]) + "t \end{array}  \right.,t∈\mathbb{R}"
o = false
m = true
i' = Translate(l, O)
t_1 = 0 (slider from 0 to 1, step 0.01)
w_1 = Vector(O, P)
P_3: O + t_1 * w_1
P_4: O + a * u + b * v + c * w + t_1 * w_1
h_1 = Vector(P_3, P_4)
text17: " t=-" + (LaTeX[d]) + ""
text16: "t=" + (LaTeX[d]) + ""