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Length in 3 Dimensions

Length in 3 Dimensions
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2019-11-22 09:37
VectorCoordinate GeometrySolid Geometry
In collections Exploring Orthogonality
This example demonstrates the calculation of the distance between two points in three-dimensional space. Key mathematical concepts include the distance formula in 3D and vectors. Using GeoGebra commands such as Plane, PointIn, Prism, etc., a 3D prism is constructed, and the diagonal length is calculated. Suitable for high school and above students to learn solid geometry.

GeoGebra Commands & Parameters

  1. Plane(A, C, B) → p
  2. PointIn(p) → w_{0}
  3. Prism(w_{2}, w_{1}, w_{0}, w_{3}, x_{0}) → a, x_3, edge7, edge4, edge5, edge9, edge1, edge8, edge6, edge10, edge2, edgeDE, x_2, edgeEF, edge3, x_1, face4, face1, face5, face6, face2, face3
  4. Segment(x_{0}, x_3) → d_{x}
  5. Segment(x_3, x_2) → d_{y}
  6. Segment(x_2, x_{0}) → d_{xy}
  7. Segment(x_2, w_{0}) → d_{z}
  8. Segment(w_{0}, x_{0}) → d_{xyz}
  9. Angle(x_2, x_3, x_{0}) → α
  10. Angle(x_{0}, x_2, w_{0}) → β
  11. Segment(x_{0}, x_2) → d_2
  12. Segment(x_{0}, w_{0}) → d

AI Drawing Prompt Reference

Draw a rectangular prism in 3D space with a base and a top face, and edges connecting the base to the top. Calculate the length of the diagonal from one vertex of the base to the opposite vertex of the top. First, draw a plane, then place a point on the plane, construct the prism, and finally calculate the diagonal length.
The prompt above was compiled from the original drawing commands and is for reference only.