MathPlotAI Logo MathPlotAI

Vector: Scalar Multiplication

Vector: Scalar Multiplication
Loading the math board and drawing, please wait…
2023-03-14 01:30
VectorCoordinate GeometryGeometric Construction
In collections geometriadinamica.es
This example illustrates the geometric meaning of scalar multiplication of vectors. Key mathematical concepts include the length change and direction preservation of vectors. Using GeoGebra commands such as Vector, Intersect, Line, and Point, the new position and length of the vector after scalar multiplication can be visually demonstrated. Suitable for high school mathematics education, particularly in coordinate geometry and vector courses.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Intersect(xAxis, yAxis) → C
  3. Line(C, u) → a
  4. Point(a) → D
  5. Vector(C, D) → v
  6. Distance(A, B) → mu
  7. Distance(C, D) → mv

AI Drawing Prompt Reference

In a coordinate plane, draw the coordinate axes and mark their intersection as the origin; plot points A and B and draw the directed segment from A to B to represent a vector; draw a line through the origin in the direction of that vector; choose a point D on this line and draw the vector from the origin to D; measure the lengths of both vectors to illustrate how scalar multiplication changes magnitude while preserving direction.
The prompt above was compiled from the original drawing commands and is for reference only.