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Geometric Interpretation of the Dot Product

Geometric Interpretation of the Dot Product
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2016-06-15 01:33
AngleVectorCoordinate GeometryGeometric Construction
In collections Multivariable Calculus
This example demonstrates the geometric relationship between the dot product of vectors and its visual representation. Key math concepts include vectors, dot product, angles, cosine theorem, and geometric constructions. GeoGebra commands/objects used are Vector, Circle, OrthogonalLine, Line, Intersect, Polygon, Angle, Segment. Suitable for high school and above students to learn about the integration of vectors and geometry.

GeoGebra Commands & Parameters

  1. Vector(P) → v
  2. Vector(Q) → u
  3. Circle((0, 0), P) → c
  4. OrthogonalLine(Q, v) → f
  5. Line((0, 0), f) → g
  6. Intersect(c, g) → D, C
  7. Line((0, 0), P) → h
  8. OrthogonalLine(C, g) → i
  9. Intersect(i, f) → B
  10. Intersect(h, f) → A
  11. Polygon(O, A, B, C) → poly1, o, a_1, b, c_1
  12. Angle(u, v) → α
  13. Segment(A, Q) → j