Vectors in GeoGebra Guide: Rotation, Length, and Angle

Vectors in GeoGebra Guide: Rotation, Length, and Angle
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2018-09-28 01:41
This example demonstrates how to create vectors in GeoGebra and perform basic operations such as rotation, measuring length, and calculating angles, providing a clear visual representation of vector geometry. Core mathematical concepts include vector definition, vector magnitude (length), vector rotation, and the angle between vectors. Construction highlights: the Vector command creates vectors, Rotate applies rotation, Length and Angle measure magnitude and angle respectively; objects include multiple text labels (text1 to text7) for points A, B, C and their rotated images A', B', as well as vector a and angle θ. Suitable for high school or early college students learning vector geometry, analytic geometry, or introductory linear algebra, and also useful for teachers preparing vector-based instructional materials.

GeoGebra Commands & Parameters

  1. Vector((0, 0), (125, 0)) → A'
  2. Rotate(A', 70°) → A
  3. Vector((x(A), y(A)), (x(A) + 100, y(A))) → B'
  4. Rotate(B', (-(30°))) → B
  5. Vector((0, 0), (x(A) + x(B), y(A) + y(B))) → C
  6. Length(C) → a
  7. Angle(C) → θ

AI Drawing Prompt Reference

Draw a vector C which is the sum of vectors A and B. First, draw a horizontal vector A' from the origin with a length of 125. Then rotate A' counterclockwise by 70 degrees to get vector A. Next, draw vector B' from the endpoint of A with a length of 100 in the same direction as A. Rotate B' counterclockwise by 30 degrees to get vector B. Finally, draw vector C from the origin, which is the sum of the endpoints of A and B. Measure the length a of vector C and the angle θ it makes with the x-axis.
The prompt above was compiled from the original drawing commands and is for reference only.