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3D Point, Vector, and Plane by Tuyetdong Phan-Yamada

3D Point, Vector, and Plane by Tuyetdong Phan-Yamada
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2020-07-21 06:46
VectorCoordinate GeometrySolid Geometry
In collections Exploring points, vectors and planes in 3D
This example demonstrates points, vectors, and planes in three-dimensional space. Key mathematical concepts include vectors, plane equations, and solid geometry. Using GeoGebra commands such as Segment, Vector, Translate, and OrthogonalPlane, you can construct points, vectors, and planes in 3D space. Suitable for high school and above students or teachers for teaching or self-study in solid geometry.

GeoGebra Commands & Parameters

  1. Segment(X, P) → f
  2. Segment(Y, P) → g
  3. Segment(A, P) → h
  4. Vector(O, N) → n_1
  5. Translate(A, n_1) → A'
  6. Vector(A, A') → n
  7. OrthogonalPlane(A, n) → p
  8. PointIn(p) → B
  9. PointIn(p) → C
  10. Vector(A, B) → u
  11. Vector(A, C) → v
  12. Angle(n, v) → t
  13. Angle(n, u) → k

AI Drawing Prompt Reference

In 3D space, place three points and connect them with segments to form a triangle. Draw a vector from the origin, then translate one of the points by that vector to get a new point, and connect the original point to the new point to form another vector. Use this vector as the normal to construct a plane through the original point. Pick two arbitrary points on the plane, and connect each to the original point to form two vectors. Finally, measure and label the angles between the normal vector and each of these two vectors.
The prompt above was compiled from the original drawing commands and is for reference only.