ModelCourses/Calculus/Vectors/Vectors in Space

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
    • Computing the dot product of two vectors
    • Computing the angle between two vectors
    • Determining two vectors are parallel or orthogonal (perpendicular) by
    • Determining the angle between two vectors is acute, or Obtuse by the sign of the dot product
  • 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

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ModelCourses/Multivariate Calculus