\\\\(
\nonumber
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\\\\(
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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
Group Exercises
- Computations of Determinants
- Parametric Representation of a Parallelogram
- Different Bases in Space
- Geometry in the Plane
- Geometry in Space
- Linear Dependence or Independence