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Review Vectors

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Agenda

  • What do we know so far?
  • Practice

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What Do We Know So Far?

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What Do We Know So Far?

  • Vectors are:
    • Direction arrows with magnitude
    • Lists of numbers
    • Mathematical objects that add using the parallelogram law

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Operations With Vectors

  • Vectors can be moved around 2-space and 3-spaced
  • Adding and subtracting vectors is with the Parallelogram Law
  • Lengths can be multiplied
  • Vectors can be “multiplied” using the dot product and cross product
  • Projection of one vector to another

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Common Formulas for Vectors

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Common Formulas for Vectors

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Applications of Vectors

  • Velocity and Forces
    • Review lesson for later
  • Vectors used as another way to define lines
    • Can be extended from 2-space to 3-space

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Vectors and Lines

  • Line definition
    • Start with a point and add some multiple of the direction vector

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  • Parametric form looks at each component of the vector form
  • Symmetric form eliminates the free variable t

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Linear Combinations and Span

  • If a vector is a linear combination of two or more other vectors, then it is linearly dependent
  • If a vector is not a linear combination of two or more other vectors, then it is linearly independent
  • The span of one or more vectors is all possible linear combinations
    • The span of a single vector is a line through the origin

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Linear Combinations and Span

  • For a vector to be in the span of other vectors is equivalent to the vector being linearly dependent on the other vectors

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Practice

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Practice

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Credits

Special thanks to all the people who made and released these awesome resources for free:

  • Presentation template by SlidesCarnival

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