Math Insight

Pages similar to: Scalar triple product example

• The scalar triple product
  Definition of the scalar triple product and derivation of its formula. Include interactive graphic to illustrate its properties.
• The cross product
  Introduction to the cross product with a focus on its basic properties. Includes an interactive graphic to illustrate these properties of the cross product.
• Cross product examples
  Examples of calculating the cross product.
• The formula for the cross product
  Derivation of the formula to calculate the cross product of two vectors.
• The dot product
  Introduction to the dot product with a focus on its basic geometric properties.
• The formula for the dot product in terms of vector components
  Derivation of the component formula for the dot product, starting with its geometric definition based on projection of vectors.
• Dot product examples
  Examples of calculating the dot product of two- and three-dimensional vectors.
• The relationship between determinants and area or volume
  The properties of the cross product and the scalar triple product give links between determinants and area or volume.
• Multiplying matrices and vectors
  How to multiply matrices with vectors and other matrices.
• Matrix and vector multiplication examples
  Examples demonstrating how to multiply matrices and vectors.
• Vectors in arbitrary dimensions
  A brief introduction to n-dimensional vectors.
• The transpose of a matrix
  Definition of the transpose of a matrix or a vector.
• Dot product in matrix notation
  How to view the dot product between two vectors as a product of matrices.
• Examples of n-dimensional vectors
  Examples showing the practical use of vectors in more than three dimensions.
• An introduction to vectors
  A introduction to the concept of a vector as an object with magnitude and direction.
• Vectors in two- and three-dimensional Cartesian coordinates
  A introduction to representing vectors using the standard Cartesian coordinate systems in the plane and in three-dimensional space.
• Introduction to changing variables in triple integrals
  Introduction to the concepts behind a change of variables in triple integrals.
• Volume calculation for changing variables in triple integrals
  A derivation of how a mapping that changes variables in triple integrals transforms volume.
• The zero vector
  The zero vector is the unique vector having zero length. The direction of the zero vector is undefined.

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