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Adding Vectors Using Component Method

Adding Vectors Using Component Method
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2019-09-11 14:06
VectorCoordinate GeometryGeometric Construction
This example demonstrates how to add vectors using the component method. Key mathematical concepts include vector decomposition and synthesis. Using GeoGebra commands such as Vector, Textfield, If, etc., it dynamically shows the components of vectors and their synthesis. Suitable for high school and above students to learn the geometric and algebraic representation of vectors.

GeoGebra Commands & Parameters

  1. Vector((MagVx, MagVy)) → V
  2. Textfield(MagVx) → InputBox1
  3. Textfield(MagVy) → InputBox2
  4. Vector((MagVx, 0)) → Vx
  5. Vector(VyStart, (MagVx, MagVy)) → Vy
  6. Angle(Vx, V) → α
  7. Vector((MagUx, MagUy)) → UPointer
  8. Textfield(MagUx) → InputBox3
  9. Textfield(MagUy) → InputBox5
  10. Vector((0, MagUy)) → UYPointer
  11. Vector((MagUx, 0)) → UXPointer
  12. Vector(UyStart, (MagVx + MagUx, MagVy + MagUy)) → Uy
  13. Vector((MagVx + MagUx, MagVy + MagUy)) → Resultant
  14. Vector(UStart, Point[(MagVx, MagVy), UPointer]) → U
  15. Vector(UStart, Point[(MagVx, MagVy), UXPointer]) → Ux
  16. Vector((0, MagVy + MagUy)) → Ry
  17. Vector((MagVx + MagUx, 0)) → RyPointer
  18. Vector((0, MagVy + MagUy), Point[(0, MagVy + MagUy), RyPointer]) → Rx
  19. Vector((1, 0)) → PosXPointer
  20. Angle(PosXPointer, Resultant) → θ
  21. Textfield(ansR) → InputBox4
  22. Textfield(ansTheta) → InputBox7
  23. If(MagR ≟ ansR, "Good Job!", " ") → text20
  24. If(ansTheta ≟ theta, "Good Job!", " ") → text19
  25. If(MagR ≟ ansR, "Good Job!", "Try Again") → text112
  26. If(abs(ansTheta - theta) ≤ 0.05, "Good Job!", "Try Again") → text113

AI Drawing Prompt Reference

Draw a vector addition demonstration. Start at the origin, use two input boxes to set the horizontal and vertical components of vector V, then draw vector V, its horizontal component Vx, and vertical component Vy, and label the angle α between V and the horizontal. Then use two input boxes for vector U's components, draw vector U starting from the tip of V, along with its horizontal component Ux and vertical component Uy. Then draw the resultant vector R from the origin to the point whose coordinates are the sum of V and U components, and label the angle θ between R and the horizontal. Finally, show two input boxes for the magnitude and angle of the resultant, and display feedback text 'Good Job!' or 'Try Again' depending on whether the inputs match the computed values.
The prompt above was compiled from the original drawing commands and is for reference only.