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Vector and Function Intersection in 3D

Vector and Function Intersection in 3D
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2017-02-09 10:45
VectorFunctionSolid Geometry
This example demonstrates the intersection of a vector and a function in three-dimensional space. Key mathematical concepts include vector operations, function graphs, and solid geometry. Using GeoGebra commands such as Point, Vector, Textfield, Sequence, and Intersect, the construction of 3D vectors and function graphs is illustrated. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Vector(A, B) → u
  3. Textfield(f) → inputBox1
  4. Sequence((i, f(i)), i, -4, 4, 1) → list3
  5. Vector((0, 0), (2, 0)) → v
  6. Sequence(Vector[(0, i), (2, f(i) / 8)], i, -4, 4, 1) → list2
  7. Intersect(f, c, 1) → G
  8. Vector(H, I) → w

AI Drawing Prompt Reference

Draw the intersection of a vector and a function in 3D space. Start by creating point A on the y-axis and then create vector u from A. Input a function expression to generate its graph, and then generate a sequence of points on the graph. From the origin, create vector v and another sequence of vectors pointing to points on the graph. Finally, find the intersection point G of the function graph with a plane and create vector w connecting two points.
The prompt above was compiled from the original drawing commands and is for reference only.