MathPlotAI Logo MathPlotAI

Equation of a Plane by Sebastian Williams

Equation of a Plane by Sebastian Williams
Loading the math board and drawing, please wait…
2015-11-24 16:24
VectorCoordinate GeometryGeometric Construction
Given three points to define a plane in space. This example constructs the plane equation using three points, involving core concepts of coordinate geometry. It uses commands like Line, Plane, OrthogonalLine, Point, Vector, suitable for high school math education or learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → d
  2. Line(A, C) → f
  3. Plane(A, B, C) → g
  4. OrthogonalLine(A, g) → h
  5. Point(h) → D
  6. Vector(A, D) → u

AI Drawing Prompt Reference

In three-dimensional space, given three points to define a plane, first draw the lines connecting the first two points and the first point to the third point. Then, construct the plane using these three points. Next, draw a line from the first point that is perpendicular to the plane, and mark a point on this line. Finally, draw a vector from the first point to this newly marked point, showing a direction vector within the plane.
The prompt above was compiled from the original drawing commands and is for reference only.