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

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* 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
** Angle of two vectors
*** Computing the dot product of two vectors
*** Computing the dot product of two vectors
*** Computing the angle between two vectors
*** Computing the angle between two vectors
*** Determining two vectors are parallel or orthogonal (perpendicular) by 
*** Determining if two vectors are parallel or orthogonal (perpendicular) when cosine of the angle is 1, -1, or 0
*** Determining the angle between two vectors is acute, or Obtuse by the sign of the dot product  
*** Determining if the angle of two vectors is acute, or obtuse when the dot product of two vectors is positive or negative
** 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
** Angle between vectors, orthogonality and cos(theta)
*** Given a particular vector, create other orthogonal vectors of desired length
*** 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 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
* The Cross Product of Two Vectors in Space

Revision as of 22:52, 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 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
    • Angle of two vectors
      • Computing the dot product of two vectors
      • Computing the angle between two vectors
      • Determining if two vectors are parallel or orthogonal (perpendicular) when cosine of the angle is 1, -1, or 0
      • Determining if the angle of two vectors is acute, or obtuse when the dot product of two vectors is positive or negative
      • Given a particular vector, create other parallel vectors of desired length
      • Given a particular vector, create other orthogonal vectors of desired length
      • Given one vector and an angle, determine another other vector with the desired angle. Maybe give part of the second vector.
  • 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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