Scalar Multiplication of a Vector
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This GeoGebra applet demonstrates the geometric meaning of multiplying a vector by a scalar. Users can adjust the scalar value using a slider to observe how the original vector v is stretched, shrunk, or reversed. Key mathematical concepts include scalar multiplication of vectors, the relationship between direction and magnitude, and intuitive understanding of linear transformations. Construction details: using Vector command to draw vector v and result vector w, Intersect command for determining vector endpoints, and a slider to control the scalar parameter. Suitable for high school mathematics vector introduction, or for visualizing linear transformation concepts in university-level linear algebra courses.
GeoGebra Commands & Parameters
Intersect(xAxis, yAxis) → AVector(A, B) → u
AI Drawing Prompt Reference
Draw a coordinate plane with a vector starting from the origin. Add a slider to control a scalar value. As the slider changes, show a second vector from the origin whose direction is the same or opposite to the original, and whose length is scaled by the scalar. Use different colors for the two vectors and label their arrows. The figure should clearly illustrate scalar multiplication: stretching when the scalar is greater than 1, shrinking when between 0 and 1, and reversing when negative.
The prompt above was compiled from the original drawing commands and is for reference only.