2D 座標架
Author: 藍邦偉  老師

$r=%v$

$A$

$ O $

$ 向量的座標表示法$
$ 加減法與係數$

1

2

3

$Step=%v$

$B$

$ \overrightarrow{OA}+\overrightarrow{OB} $

$ \overrightarrow{OA}-\overrightarrow{OB} $

$ r\;\overrightarrow{OA}

e = 1.5 (slider from -5 to 5, step 0.1)
A_0 = (2.476933065090967, 1.722389656933101)
A = DynamicCoordinates(A_0, floor(x(A_0)), floor(y(A_0)))
t2 = 0 (slider from 0 to 1, step 0.01)
O = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
a = false
b = false
c = false
s = 0 (slider from 0 to If[a ≟ true, 3, If[b ≟ true, 5, 2]], step 1)
t1 = 0 (slider from 0 to 1, step 0.01)
t3 = 0 (slider from 0 to 1, step 0.01)
t4 = 0 (slider from 0 to 1, step 0.01)
t5 = 0 (slider from 0 to 1, step 0.01)
B_0 = (1.5793225681498302, 3.0019617918710657)
B = DynamicCoordinates(B_0, floor(x(B_0)), floor(y(B_0)))
u_0 = Vector(O, A)
v_0 = Vector(O, B)
A_1: O + t1 * Vector[O, A]
B_1: O + t1 * Vector[O, B]
u_1 = Vector(O, A_1)
C = Point(u_1)
v_1 = Vector(C, B_1)
t_A: "$ A" + (LaTeX[A]) + " $"
t_B: "$ B" + (LaTeX[B]) + " $"
O_2: O + t2 * Vector[O, B]
A_2: A + t2 * Vector[O, B]
u_2 = Vector(O_2, A_2)
poly2, a_2, o_2, o, a_1 = Polygon(A_2, O_2, O, A)
C_3: O + t3 * Vector[O, A_2]
u_3 = Vector(O, C_3)
a_3 = Segment(A_2, B)
b_3 = Segment(A_2, A)
B_b: O - t2 * Vector[O, B]
u = Vector(O, B_b)
O_3: O + t3 * Vector[O, A]
B_c: B_b + t3 * Vector[O, A]
v = Vector(O_3, B_c)
poly3, b_c, b_b, o_1, o_3 = Polygon(B_c, B_b, O, O_3)
B_d: O + t4 * Vector[O, B_c]
w = Vector(O, B_d)
O_5: O + t5 * Vector[O, B]
B_5: B_d + t5 * Vector[O, B]
z = Vector(O_5, B_5)
text1: "$ " + (LaTeX[B_b]) + " $"
text2: "$ " + (LaTeX[B_c]) + " $"
text3: "$ " + (LaTeX[B_d]) + " $"
text4: "$ " + (LaTeX[B_5]) + " $"
poly5, o_4, o_5, b_5, b_d = Polygon(O, O_5, B_5, B_d)
D_0 = (1.2737530372762518, 2.73458850994373)
text5: "$ " + (LaTeX[A_2]) + " $"
text6: "$ " + (LaTeX[C_3]) + " $"
K: O + t2 * e * Vector[O, A]
d = Vector(O, K)
f = Vector(O, K)
text7: "$ " + (LaTeX[K]) + " $"