Pages similar to: Vectors in two- and three-dimensional Cartesian coordinates
- An introduction to vectors
A introduction to the concept of a vector as an object with magnitude and direction. - 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 scalar triple product
Definition of the scalar triple product and derivation of its formula. Include interactive graphic to illustrate its properties. - Scalar triple product example
Example showing how to calculate the scalar triple product. - 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. - 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. - Cartesian coordinates
Illustration of Cartesian coordinates in two and three dimensions. - Lines (and other items in Analytic Geometry)
How to describe the equation for a line in terms of horizontal and vertical coordinates. - The zero vector
The zero vector is the unique vector having zero length. The direction of the zero vector is undefined.