標準單位向量的外積
Author: 藍邦偉  老師

x

y

z

單位向量

座標軸

 \overrightarrow{i} ×\overrightarrow{j}=\overrightarrow{k}

\overrightarrow{j}×\overrightarrow{k}=\overrightarrow{i}

\overrightarrow{k}×\overrightarrow{i}=\overrightarrow{j}

\overrightarrow{j}×\overrightarrow{i}=-\overrightarrow{k}

\overrightarrow{k}×\overrightarrow{j}=-\overrightarrow{i}

\overrightarrow{i}×\overrightarrow{k}=-\overrightarrow{j}

|\overrightarrow{i}×\overrightarrow{j}|

|\overrightarrow{j}×\overrightarrow{k}|

|\overrightarrow{k}×\overrightarrow{i}|

\overrightarrow{i}

\overrightarrow{j}

\overrightarrow{k}

-\overrightarrow{i}

-\overrightarrow{k}

-\overrightarrow{j}

標準單位向量的外積

α = 4.1887902047863905 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
β = 1.5009831567151233 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O = (8.737738484759573, 4.209402583212538)
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 = 6 (slider from 1 to 10, step 1)
a = Vector(O - L * v, O + L * v)
b = Vector(O - L * w, O + L * w)
z = Vector(O - L * u, O + L * u)
A_1: O + L * u
B_1: O + L * v
Z: O + L * w
c = false
d = false
Q_2: 0.23 * Corner[2] + 0.77 * 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)
r = 5 (slider from 0.1 to 6)
P_1: O + r * u
P_2: O + r * v
P_3: O + r * w
a_1 = Vector(O, P_1)
a_2 = Vector(O, P_2)
a_3 = Vector(O, P_3)
P_4: O - r * u
P_5: O - r * v
P_6: O - r * w
a_4 = Vector(O, P_4)
a_5 = Vector(O, P_5)
a_6 = Vector(O, P_6)
A = (-0.6760427531980934, 7.178702740044975)
n = 1 (slider from 0 to 9, step 1)
Z1, o, p_1, h, p_2 = Polygon(O, P_1, P_1 + P_2 - O, P_2)
Z2, o_1, p_3, i, p_4 = Polygon(O, P_3, P_3 + P_2 - O, P_2)
Z3, o_2, p_5, j, p_6 = Polygon(O, P_3, P_3 + P_1 - O, P_1)

Tool: Poly_B3
Input: A, B, C
Output: poly1'

α = Angle(C, B, A)
d: sqrt(sgn(sin(α)))
A' = Dilate(A, d, A)
B' = Dilate(B, d, A)
C' = Dilate(C, d, A)
poly1', c', a', b' = Polygon(A', B', C')

Tool: Poly_B5
Input: A, B, C, D, E
Output: poly1'

poly1, a, b, c, d, e = Polygon(A, B, C, D, E)
F = Midpoint(b)
G = Midpoint(d)
α = Angle(G, F, A)
f: sqrt(sgn(sin(α)))
A' = Dilate(A, f, A)
B' = Dilate(B, f, A)
C' = Dilate(C, f, A)
D' = Dilate(D, f, A)
E' = Dilate(E, f, A)
poly1', a', b', c', d', e' = Polygon(A', B', C', D', E')