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Cross Product and Cauchy-Binet Parallelograms

Cross Product and Cauchy-Binet Parallelograms
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2018-03-15 03:36
VectorCoordinate GeometryGeometric Construction
This example illustrates the concept of cross product and Cauchy-Binet parallelograms. By constructing vectors u and v, and their cross product vector w, a parallelogram is formed. Commands used include Intersect, Vector, Polygon, Angle, and Centroid. Suitable for high school mathematics education, particularly in coordinate geometry and vector topics.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. Vector(A, B) → u
  3. Vector(A, C) → v
  4. Polygon(A, B, D, C) → q1, a, b, d, c
  5. Angle(C, A, E) → α
  6. Angle(B, A, E) → β
  7. Centroid(q1) → F
  8. Polygon((x(A), y(A), 0), (x(B), y(B), 0), (x(D), y(D), 0), (x(C), y(C), 0)) → q2, f, g, h, i
  9. Polygon((x(A), 0, z(A)), (x(B), 0, z(B)), (x(D), 0, z(D)), (x(C), 0, z(C))) → q3, j, k, l, m
  10. Polygon((0, y(A), z(A)), (0, y(B), z(B)), (0, y(D), z(D)), (0, y(C), z(C))) → q4, n, p, q, r
  11. Centroid(q2) → G
  12. Centroid(q3) → H
  13. Centroid(q4) → I