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Week 6, Short Day: Geometry in the Plane and in 3D Space

Today we continue with concepts such as linear combinations, linear independence, basis and coordinates. Our subjects will also involve some repetition of knowledge from highschool about vectors in standard coordinate systems in the plane and in 3D space. Determinants emerge repeatedly as useful tools.

Today’s Key Concepts
Linear combinations. Linear dependence and independence. Change of coordinates when the base is changed. Standard bases and the standard coordinate systems. Dot product. Projection of vectors onto vectors. Cross product.

Preparation and Syllabus
Today we continue with the subjects from eNote 9 Determinants and eNote 10 Geometric Vectors.

Maple Ressources

  • DotProduct or simply . computes the dot product of two vectors.
  • CrossProduct computes the cross product of two 3D vectors.

Today’s Maple demo is DotAndCrossProduct.

Activity Program

  • 13.00 – 14.00: $\,$No live lecture today (lecturer is absent). See the pre-recorded lecture on this link, or show up as usual in Auditorium 42 at 13:00 where the recording will be shown on the screen. Alternatively, you can watch the lecture from last year by David Brander or from two years ago by Jesper Kampman.
  • 14.00 – 16.00: $\,$Group exercises in the study areas (b. 302, bottom floor)
  • 16.00 – 17.00: $\,$Weekly Test.

Group Exercises

  1. Computations of Determinants
  2. Parametric Representation of a Parallelogram
  3. Different Bases in Space
  4. Geometry in the Plane
  5. Geometry in Space
  6. Linear Dependence or Independence