三维空间向量的分解与表示

GeoGebra 命令及参数

1. Line(C, xAxis) → f
2. Line(B, yAxis) → g
3. Intersect(f, g) → A
4. Line(A, zAxis) → h
5. Line(C, zAxis) → i
6. Line(B, zAxis) → j
7. Line(M, xAxis) → k
8. Line(M, yAxis) → l
9. Line(D, xAxis) → m
10. Line(D, yAxis) → n
11. Intersect(k, n) → E
12. Intersect(l, m) → F
13. Translate(O, Vector[(If[b < 5, b / 5, 1] * Vector[O, C])]) → O'
14. Vector(O, O') → u
15. Translate(C, Vector[(If[b ≤ 5, 0, If[5 ≤ b < 10, (b - 5) / 5, 1]] * Vector[C, A])]) → C'
16. Vector(O', C') → v
17. Translate(A, Vector[(If[b ≤ 10, 0, If[10 < b < 15, (b - 10) / 5, 1]] * Vector[A, M])]) → A'
18. Vector(A, A') → w
19. Segment(D, E) → p
20. Segment(E, M) → q
21. Segment(M, F) → r
22. Segment(D, F) → s
23. Segment(M, A) → t
24. Segment(F, B) → e
25. Segment(O, D) → g_1
26. Segment(A, B) → d
27. Segment(E, C) → b_{1}
28. Segment(C, A) → c_{1}
29. Segment(C, O) → f_1
30. Translate(O, Vector[(If[a < 5, a / 5, 1] * Vector[O, B])]) → O'_{1}
31. Vector(O, O'_{1}) → u_1
32. Translate(A, Vector[(If[a ≤ 10, 0, If[10 < a < 15, (a - 10) / 5, 1]] * Vector[A, M])]) → A'_{1}
33. Translate(B, Vector[(If[a ≤ 5, 0, If[5 ≤ a < 10, (a - 5) / 5, 1]] * Vector[B, A])]) → B'
34. Vector(B, B') → v_1
35. Vector(A, A'_{1}) → w_1
36. Translate(O, Vector[(If[c < 5, c / 5, 1] * Vector[O, D])]) → O'_{2}
37. Vector(O, O'_{2}) → d_1
38. Translate(D, Vector[(If[c ≤ 5, 0, If[5 ≤ c < 10, (c - 5) / 5, 1]] * Vector[D, F])]) → D'
39. Vector(D, D') → e_1
40. Translate(F, Vector[(If[c ≤ 10, 0, If[10 < c < 15, (c - 10) / 5, 1]] * Vector[F, M])]) → F'
41. Vector(F, F') → h_1
42. Vector(O, M) → i_1
43. Midpoint(O, O'_{1}) → I
44. Midpoint(B, B') → J
45. Midpoint(A, A'_{1}) → K