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Airplane Vectors

Airplane Vectors
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2015-07-16 07:44
AngleVectorCoordinate GeometryGeometric Construction
This example demonstrates the distance between two planes that leave the same point simultaneously. It involves core math concepts like vectors, angles, rotation, and coordinate geometry. Constructed using GeoGebra commands such as Intersect, Vector, Angle, and Rotate. Suitable for high school students learning vector and kinematics.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Vector(B, A) → A_{vector}
  3. Vector(O, B) → B_{vector}
  4. Vector(O, A) → Result
  5. Angle(Segment[O, (5, 0)], Segment[O, A]) → O_{angle}
  6. CircleArc(O, (25, 0), A) → arc
  7. Corner(pic2, 4) → A_4
  8. Corner(pic1, 3) → B_3
  9. Corner(pic1, 4) → B_4
  10. Midpoint(B_1, B_3) → B_c
  11. Corner(pic2, 3) → A_3
  12. Midpoint(A_1, A_3) → A_c
  13. Polygon(B_1, B_2, B_3, B_4) → poly1, b_1, b_2, b_3, b_4
  14. Polygon(A_1, A_2, A_3, A_4) → poly2, a_1, a_2, a_3, a_4
  15. PointIn(poly1) → C
  16. Rotate(pic1, α, B_c) → pic1'
  17. Rotate(pic2, α, A_c) → pic2'
  18. Angle(Result) → test
  19. Rotate(pic2, Angle[Result] - 90°, A_c) → pic2''

AI Drawing Prompt Reference

Draw a graph of two plane vectors leaving the same point. The first vector points from the origin to point B, and the second vector points from the origin to point A. Draw the angle between these vectors and a circle arc. Construct a quadrilateral and another quadrilateral, then find the center points of both quadrilaterals. Rotate the first quadrilateral around its center point and rotate the second quadrilateral around its center point. Finally, adjust the rotation angle of the second quadrilateral based on the result to maintain the desired geometric relationship.
The prompt above was compiled from the original drawing commands and is for reference only.