Vector Addition & Subtraction #2: Geometric Construction with Mirror

Vector Addition & Subtraction #2: Geometric Construction with Mirror
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2017-04-20 20:05
① This GeoGebra example dynamically demonstrates the geometric meaning of vector addition (w = u + v) and subtraction (z = u - v) for two vectors u and v, using the Mirror command to construct a reflected vector v' and visually illustrating the parallelogram and triangle laws. ② Core mathematical concepts include vector addition, subtraction, opposite vectors, vector equality, and transformations such as reflection, all within the context of scalene triangles. ③ Construction details: from the summary, the Vector command creates vectors u, v, w, v', and z; the Mirror command reflects vector v to obtain v'; text objects text1, text2, text3 label vectors or results; points A and B serve as endpoints or origins. ④ Suitable for high school or early college students learning vector operations geometrically, and for teachers demonstrating vector addition/subtraction properties, especially the relationship between subtraction and opposite vectors.

GeoGebra Commands & Parameters

  1. Vector(A) → u
  2. Vector(A, B) → v
  3. Mirror(v, A) → v'