MathPlotAI Logo MathPlotAI

Cube and Vector Relationship Demonstration

Cube and Vector Relationship Demonstration
Loading the math board and drawing, please wait…
2021-08-21 12:09
VectorCoordinate GeometrySolid GeometryGeometric Construction
In collections Mapping Diagrams: From AB to C&DE, Resource
This example demonstrates the relationship between points, vectors, and faces in a cuboid. Core math concepts include vectors, coordinate geometry, and solid geometry. Construction highlights involve commands like If, Point, Vector, Textfield, Segment, Zip, Element, and Midpoint to create geometric objects such as points, vectors, segments, and midpoints, forming the cuboid and related elements. Suitable for high school students and math enthusiasts learning solid geometry and vector concepts.

GeoGebra Commands & Parameters

  1. If((D2 * F2) < 0, A2, C2) → A3
  2. If((E2 * F2) < 0, B2, C2) → B3
  3. If((E3 * F3) < 0, B3, C3) → B4
  4. If((D3 * F3) < 0, A3, C3) → A4
  5. If((E4 * F4) < 0, B4, C4) → B5
  6. If((D4 * F4) < 0, A4, C4) → A5
  7. If((E5 * F5) < 0, B5, C5) → B6
  8. If((D5 * F5) < 0, A5, C5) → A6
  9. If((E6 * F6) < 0, B6, C6) → B7
  10. If((D6 * F6) < 0, A6, C6) → A7
  11. If((E7 * F7) < 0, B7, C7) → B8
  12. If((D7 * F7) < 0, A7, C7) → A8
  13. If((E8 * F8) < 0, B8, C8) → B9
  14. If((D8 * F8) < 0, A8, C8) → A9
  15. If((E9 * F9) < 0, B9, C9) → B10
  16. If((D9 * F9) < 0, A9, C9) → A10
  17. If((E10 * F10) < 0, B10, C10) → B11
  18. If((D10 * F10) < 0, A10, C10) → A11
  19. If((E11 * F11) < 0, B11, C11) → B12
  20. If((D11 * F11) < 0, A11, C11) → A12
  21. If((E12 * F12) < 0, B12, C12) → B13
  22. If((D12 * F12) < 0, A12, C12) → A13
  23. If((E13 * F13) < 0, B13, C13) → B14
  24. If((D13 * F13) < 0, A13, C13) → A14
  25. If((E14 * F14) < 0, B14, C14) → B15
  26. If((D14 * F14) < 0, A14, C14) → A15
  27. If((E15 * F15) < 0, B15, C15) → B16
  28. If((D15 * F15) < 0, A15, C15) → A16
  29. If((E16 * F16) < 0, B16, C16) → B17
  30. If((D16 * F16) < 0, A16, C16) → A17
  31. If((E17 * F17) < 0, B17, C17) → B18
  32. If((D17 * F17) < 0, A17, C17) → A18
  33. If((E18 * F18) < 0, B18, C18) → B19
  34. If((D18 * F18) < 0, A18, C18) → A19
  35. If((E19 * F19) < 0, B19, C19) → B20
  36. If((D19 * F19) < 0, A19, C19) → A20
  37. If((E20 * F20) < 0, B20, C20) → B21
  38. If((D20 * F20) < 0, A20, C20) → A21
  39. If((E21 * F21) < 0, B21, C21) → B22
  40. If((D21 * F21) < 0, A21, C21) → A22
  41. If((E22 * F22) < 0, B22, C22) → B23
  42. If((D22 * F22) < 0, A22, C22) → A23
  43. If((E23 * F23) < 0, B23, C23) → B24
  44. If((D23 * F23) < 0, A23, C23) → A24
  45. If((E24 * F24) < 0, B24, C24) → B25
  46. If((D24 * F24) < 0, A24, C24) → A25
  47. Point(yAxis) → x_0
  48. Vector(x_0, B) → u
  49. Textfield(f) → inputBox1
  50. Textfield(f) → inputBox2
  51. Textfield(a) → inputBox3
  52. Segment((0, Element[a_*, n]), (0, Element[b_*, n])) → c
  53. Textfield(b) → inputBox4
  54. Zip((0, b), b, b_*) → bMD
  55. Zip((a, f(a)), a, b_*) → bGraphpts
  56. Zip(Vector[(0, a), (2, (y_{zoom} * f(a)))], a, b_*) → bArrowMD
  57. Zip(Vector[(0, V), (2, (y_{zoom} * f(V)))], V, a_*) → aArrowMD
  58. Zip((V, f(V)), V, a_*) → aGraphpts
  59. Zip((0, V), V, a_*) → aMD
  60. Zip((2, (y_{zoom} * f(V))), V, a_*) → faMD
  61. Zip((2, (y_{zoom} * f(V))), V, b_*) → fbMD
  62. Element(aMD, n) → a_n
  63. Element(bMD, n) → b_n
  64. Element(aArrowMD, n) → aArr_n
  65. Element(bArrowMD, n) → bArr_n
  66. Element(bGraphpts, n) → bgr_n
  67. Element(aGraphpts, n) → agr_n
  68. Element(faMD, n) → fa_n
  69. Element(fbMD, n) → fb_n
  70. Segment((y(a_n), 0), (y(b_n), 0)) → d
  71. Midpoint(c) → m_n
  72. Midpoint(d) → mgr_1
  73. Vector(m_n, fm_n) → mArr_n

AI Drawing Prompt Reference

Draw a cuboid and demonstrate the relationship between vectors and its faces. First, determine the vertices of the cuboid. Then, create vectors from the origin to each vertex. Next, draw the faces of the cuboid and mark the intersection points of the vectors with the faces. Finally, add text to explain the relationship between the vector directions and the face planes, making the entire graphic clear and understandable.
The prompt above was compiled from the original drawing commands and is for reference only.