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Area of a Parallelogram and Cross Product

Area of a Parallelogram and Cross Product
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2017-04-25 18:14
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the area of a parallelogram using the cross product of vectors. Key math concepts include vector cross product, parallelogram area formula, and vector magnitude. GeoGebra commands like Vector, Line, Intersect, Segment, Polygon, OrthogonalLine, Angle, Midpoint, Distance, and PointIn are used to construct the figure and perform calculations. Suitable for high school mathematics education to understand the application of vector cross product in geometric calculations.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(A, C) → v
  3. Line(B, v) → f
  4. Line(C, u) → g
  5. Intersect(g, f) → D
  6. Segment(C, D) → h
  7. Segment(B, D) → i
  8. Polygon(A, B, D, C) → poly1, a, b, d, c
  9. Vector(A, E) → w
  10. OrthogonalLine(C, a, space) → j
  11. Intersect(j, a) → F
  12. Segment(C, F) → k
  13. Angle(C, F, A) → α
  14. Midpoint(A, C) → G
  15. Midpoint(A, B) → I
  16. Distance(A, E) → distanceAE
  17. PointIn(poly1) → Pointpoly1
  18. Midpoint(C, B) → H
  19. Midpoint(E, A) → J
  20. Angle(C, A, B) → β