ModelCourses/Calculus/Vectors/Vectors in Space: Difference between revisions

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** Expressing a vector from Point A to Point B in vector notation
** Expressing a vector from Point A to Point B in vector notation
** Sketching a position vector
** Sketching a position vector
** Vector algebra: (1) scalar multiplication; (2) vector addition and substraction
** Vector algebra: (1) scalar multiplication; (2) vector addition and subtraction
** Magnitude and 2-norm of a vector, unit vector
*** Computing a scalar times a vector and a sum (difference) of two vectors
*** Sketching and sketching a scalar times a vector and a sum (difference) of two vectors
** Triangle inequality
** Triangle inequality


* The Dot Product of Two Vectors
* The Dot Product of Two Vectors
** Two definitions of dot product of two vectors
** Two definitions of dot product of two vectors
*** Calculating the standard collection of numerical examples
*** Calculating numerically  examples
** Parallel and geometric implications
** Parallel and geometric implications
*** Given a particular vector, create other parallel vectors of desired length
*** Given a particular vector, create other parallel vectors of desired length

Revision as of 21:49, 21 December 2011

Vectors in Space

  • Vector Algebra
    • Expressing a vector from Point A to Point B in vector notation
    • Sketching a position vector
    • Vector algebra: (1) scalar multiplication; (2) vector addition and subtraction
      • Computing a scalar times a vector and a sum (difference) of two vectors
      • Sketching and sketching a scalar times a vector and a sum (difference) of two vectors
    • Triangle inequality
  • The Dot Product of Two Vectors
    • Two definitions of dot product of two vectors
      • Calculating numerically examples
    • Parallel and geometric implications
      • Given a particular vector, create other parallel vectors of desired length
    • Angle between vectors, orthogonality and cos(theta)
      • Given two vectors, determine the angle between
      • Given one vector and an angle, determine another other vector with the desired angle. Maybe give part of the second vector.
      • Given one 2d vector, determine another vector which is orthogonal
  • The Cross Product of Two Vectors in Space
    • Calculating the standard collection of numerical examples
    • Orthogonality
      • Given a vector, determine another vector which is orthogonal
    • Orthogonality between three vectors
      • Given two vectors, determine a vector which is normal

Download the set definition file for this problem set

ModelCourses/Multivariate Calculus

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