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Subtracting Vectors in 1D, 2D, and 3D

Subtracting Vectors in 1D, 2D, and 3D
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2020-11-12 01:21
VectorCoordinate GeometryGeometric Construction
This example demonstrates vector subtraction in one, two, and three dimensions. Key mathematical concepts include basic vector operations. Using GeoGebra commands such as Vector, button, and text, the process of vector subtraction is visually illustrated. Suitable for high school and above students learning vector operations.

GeoGebra Commands & Parameters

  1. Vector((-1 + (3 * t), -0.5 - (0.5 * t)), ((3 * t), (-0.5 * t))) → v2
  2. Vector((0, 0), (-2, 0)) → u1
  3. Vector((-2 + (6 * t), 0), ((6 * t), 0)) → u2
  4. Vector((0, 0.1), (6, 0.1)) → u3
  5. Vector((1 + (2 * t), 1, -3 + (4 * t)), ((2 * t), 0, (4 * t))) → w2

AI Drawing Prompt Reference

Create a coordinate system showing vector subtraction in 2D and 3D. In 2D, draw a vector from the origin to (-2,0), then another vector from that endpoint with direction depending on parameter t, representing the subtracted vector. Also draw a vector from origin along positive x-axis, and a second vector from its endpoint along x-axis, illustrating subtraction. In 3D, draw a vector starting at (1,1,-3) with endpoint at (2t,0,4t), showing three-dimensional subtraction. Use arrows for vectors and add text labels explaining the subtraction.
The prompt above was compiled from the original drawing commands and is for reference only.