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Triple Product Rule Cube

Triple Product Rule Cube
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2018-09-19 07:35
VectorSolid GeometryGeometric Construction
This example demonstrates the geometric application of the triple product rule in a cube, visualizing the calculation of the scalar triple product through 3D vectors. Core mathematical concepts include vectors, solid geometry, scalar triple product operations, and spatial geometric relationships. GeoGebra commands and objects used in construction are Intersect, Point, Cube, Polygon, and Segment, with objects like points A, B, C, and face ABCD. Suitable for high school and above students studying solid geometry, vector algebra, and spatial vector products, it serves as an educational tool for demonstrating geometric intuition and understanding.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, yAxis) → A
  2. Point(zAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Polygon(B, A, D, C) → q1, b, a_1, d, c
  6. Point(zAxis) → I
  7. Point(Circle[I, Distance[A, I], Segment[A, I]]) → J
  8. Cube(A, I, J) → e, K, faceJKON, faceLMNO, edgeAK, edgeAI, edgeIJ, edgeJK, edgeAL, edgeKO, edgeLO, edgeLM, L, edgeIM, edgeMN, edgeJN, edgeNO, M, N, O, faceAIJK, faceAKOL, faceAIML, faceIJNM
  9. Segment(A, K) → f
  10. Point(edgeJK) → P
  11. Point(edgeNO) → Q
  12. Point(edgeLM) → R
  13. Segment(Q, P) → g
  14. Segment(Q, R) → h
  15. Segment(P, C) → i
  16. Segment(R, F) → j
  17. Point(edgeIM) → S
  18. Point(edgeIJ) → T
  19. Segment(S, F) → k
  20. Segment(T, C) → l
  21. Point(edgeMN) → U
  22. Point(edgeJN) → V
  23. Segment(S, V) → m
  24. Segment(T, U) → n
  25. Point(edgeKO) → W
  26. Point(edgeLO) → Z
  27. Point(edgeAL) → A_1
  28. Segment(W, A_1) → p
  29. Point(f) → B_1
  30. Segment(Z, B_1) → q
  31. Segment(U, Z) → r
  32. Intersect(r, h) → C_1
  33. Segment(C_1, G) → s
  34. Segment(V, W) → t
  35. Intersect(g, t) → D_1
  36. Segment(D_1, G) → f_1
  37. Intersect(m, n) → E_1
  38. Segment(E_1, G) → g_1

AI Drawing Prompt Reference

Draw a cube with points A, B, C, and face ABCD. First, create point A at the intersection of the z-axis and y-axis. Then, create point C on the circle with diameter AB. Use points A, B, and C to construct cube a. Draw face ABCD and connect points A, B, C, and D. Next, create point I on the z-axis and point J on the circle with diameter AI. Use points A, I, and J to construct cube e and connect points A, I, J, and K. Draw face AIJK and connect points A, I, J, and K.
The prompt above was compiled from the original drawing commands and is for reference only.