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Magnitude and Direction of Vector v=PQ

Magnitude and Direction of Vector v=PQ
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2015-06-16 04:02
VectorCoordinate GeometryGeometric Construction
In collections CCSS Honors Math II Topic 2
This example constructs vector v=PQ from point P(7, -2) to point Q(1, 1) and demonstrates how to find the magnitude of the vector and describe its direction. It uses commands like Segment, Vector, Angle, and Product in GeoGebra, suitable for high school vector mathematics.

GeoGebra Commands & Parameters

  1. Product(Zip[Element[f, 1]^(Mod[Element[f, 2], 2]), f, Factors[m2]]) → m2sf
  2. Angle(P2, P1, P0) → α
  3. Segment(P0, P1) → a
  4. Segment(P1 + (0, (-0.5)), P2 + (0, (-0.5))) → b1
  5. Segment(P1, P2) → b
  6. Segment(P0 - (0.5, 0), P1 - (0.5, 0)) → a1
  7. GCD(v1, v2) → CommFact
  8. Vector(P, Q) → v
  9. TableText({{Formula2a, "\textsf{Magnitude formula from the Pythagorean Theorem}"}, {Formula2b, "\textsf{Substitute.}"}, {Formula2c, "\textsf{Simplify.}"}, {Formula2d, " "}}, "l") → work2
  10. TableText({{Formula2e, "\textsf{Magnitude formula from the distance formula}"}, {Formula2f, "\textsf{Substitute.}"}, {Formula2b, "\textsf{Simplify.}"}, {Formula2d, " "}}, "l") → work3