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Exploring Vectors in 3-Dimensions

Exploring Vectors in 3-Dimensions
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2013-10-14 02:16
VectorCoordinate GeometrySlider Animation
This applet allows students to explore the effects of changing the components of a vector in 3-space. By adjusting the x, y, and z components, students can observe changes in the vector's direction and magnitude. Commands used include Line, Segment, Vector, Point, and Intersect. Suitable for high school and above students learning about 3D vectors.

GeoGebra Commands & Parameters

  1. Line(O, z_1) → a
  2. Line(O, x_1) → b
  3. Line(O, y_1) → c
  4. Segment(O, y_2) → e
  5. Segment(y_2, A) → g
  6. Segment(A, B) → h
  7. Vector(O, B) → u
  8. Segment(C, H) → i
  9. Point(g) → I
  10. Segment(C, I) → j
  11. Segment(D, J) → k
  12. Segment(D, K) → l
  13. Segment(y_2, E) → d
  14. Segment(E, F) → f
  15. Vector(O, F) → v
  16. Segment(y_{13}, E_1) → d_1
  17. Segment(A_1, B_1) → h_1
  18. Segment(O, y_{-2}) → m
  19. Vector(O, B_1) → w
  20. Segment(A_2, B_2) → h_2
  21. Segment(z_{-3}, G) → n
  22. Segment(G, L) → p
  23. Vector(O, L) → z
  24. Segment(O, x_{-1}) → q
  25. Segment(x_{-1}, M) → r
  26. Segment(M, N) → s
  27. Vector(O, N) → t
  28. Segment(x_{-1}, P) → b_1
  29. Segment(P, Q) → c_1
  30. Vector(O, Q) → u_1
  31. Intersect(d_1, h_1) → R
  32. Segment(R, S) → a_1
  33. Vector(O, S) → v_1
  34. Segment(y_{-2}, T) → e_1
  35. Segment(T, U) → f_1
  36. Vector(O, U) → w_1

AI Drawing Prompt Reference

Draw a vector in 3D space and adjust its direction and magnitude by changing the sliders for x, y, and z. First, draw the x, y, and z axes, then create vector u from the origin to point B, and finally draw line segment CI and vector v from the origin to point F.
The prompt above was compiled from the original drawing commands and is for reference only.