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Vector Addition by Ku, Yin Bon (Albert)

Vector Addition by Ku, Yin Bon (Albert)
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2015-08-18 17:24
VectorCoordinate GeometryGeometric Construction
This example demonstrates the geometric construction of vector addition. It involves core mathematical concepts such as vectors, geometric construction, and the fundamental theorem of vector algebra. The construction uses commands like Vector, Segment, Translate, and Polygon in GeoGebra to create vectors, line segments, translations, and polygons. It is suitable for high school mathematics teaching and understanding vector operations.

GeoGebra Commands & Parameters

  1. Vector(O, P) → u
  2. Segment(O, (xp, 0, 0)) → a
  3. Segment((xp, 0, 0), (xp, yp, 0)) → b
  4. Segment((xp, yp, 0), P) → c
  5. Vector(O, Q) → v
  6. Translate(Q, u) → Q'
  7. Vector(P, Q') → w
  8. Vector(O, Q') → d
  9. Segment(P, (xp + xq, yp, zp)) → e
  10. Segment((xp + xq, yp, zp), (xp + xq, yp + yq, zp)) → f
  11. Segment((xp + xq, yp + yq, zp), Q') → g
  12. Polygon(Q, Q', P, (0, 0, 0)) → poly1, i, j, k, l

AI Drawing Prompt Reference

Draw two 3D vectors from the origin to points P and Q, each decomposed into three mutually perpendicular segments along the x, y, and z axes; translate the first vector to the tip of the second to obtain point Q′, connect P to Q′ to show the resultant vector, and complete the parallelogram O‑P‑Q′‑Q while displaying the component segments of both vectors.
The prompt above was compiled from the original drawing commands and is for reference only.