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Cross Product Illustration

Cross Product Illustration
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2019-12-07 03:00
VectorSolid GeometryCalculus
This example illustrates the concept of the cross product. The cross product is a vector operation in three dimensions, resulting in a vector perpendicular to the original vectors. The construction uses Vector, OrthogonalPlane, Polygon, Circle, Segment, Point, Angle, etc., GeoGebra commands to build a geometric representation of the cross product. Suitable for high school mathematics education and learning three-dimensional vector operations.

GeoGebra Commands & Parameters

  1. Vector(O, A) → u
  2. Vector(O, B) → v
  3. OrthogonalPlane(O, Vector[u ⊗ v]) → p
  4. Polygon(O, A, F, B) → q1, o, a, f, b_1
  5. Circle(H, I) → d
  6. Segment(H, J) → g
  7. Segment(H, K) → h
  8. Polygon(L, M, N, P) → q2, l, m, n, p_1
  9. Point(g) → Q
  10. Circle(Q, R) → k
  11. Segment(Q, S) → i
  12. Polygon(T, U, V, W) → q3, t, u_1, v_1, w_1
  13. Polygon(Z, A_1, B_1, C_1) → q4, z_1, a_1, j, c_1
  14. Point(g) → D_1
  15. Circle(D_1, E_1) → r
  16. Segment(D_1, F_1) → s
  17. Polygon(G_1, H_1, I_1, J_1) → q5, g_1, h_1, i_1, j_1
  18. Angle(w, u) → α
  19. Angle(w, v) → β