Vector Geometry

NOTICE: The Vector Geometry page will be deleted and all linked pages will be moved to the Linear Algebra page in the next couple of days - June 8th, 2014 |

*This section is fairy rigorous when it comes to mathematical proofs and theorems. Please check the Proof Guide first so that you won't get lost!*

Welcome to the ** Vector Geometry** page.

Here you will be able to browse a large variety of *Vector Geometry* topics. It is recommended that you are familiar with the following sections before continuing on into the *Vector Geometry* portion of this site:

## Necessary to Know:

- Solving for unknown variables
- Linear Equations
- Slope of Linear Equations
- 2D and 3D Shape Geometry
- Unit Circle, Trigonometry

# Pretest

Not sure if you are ready to jump into the topics listed below? Then take the Vector Geometry Pretest to evaluate your skills before moving into the more challenging topics below!

# Preamble

This section is rigorous in proofs regarding the formulae derived.

- Vector Notation
- Definition of a Vector and of a Scalar
- 2-Space, 3-Space, Euclidean n-Space, 1-Space
- Basic Properties of Vectors
- Determining a Vector Given Two Points
- Translation Equations
- Norm of a Vector
- Unit Vectors
- Vector Dot Product (Euclidean Inner Product)
- Orthogonal (Perpendicular) Vectors
- Orthogonal Projections
- Vector Cross Product
- Lagrange's Identity
- Standard Unit Vectors
- Area of a Parallelogram in R3, and Area of a Triangle
- Area of a Parallelogram in 2-Space and Volume of a Parallelepiped in 3-Space
- Scalar Triple Product
- Vectors that Lie on the Same Plane
- Point-Normal Form Equations of a Plane
- Vector Form Equations of a Plane
- Parametric Equations of Lines
- Lines of Intersection Between Two Planes
- Distance Between a Plane and a Point
- Distance Between Parallel Planes

- Cauchy-Schwarz Inequality
- Triangle Inequality
- Distance Between Vector
- Vector Pythagorean Theorem
- Matrix Notation for Vectors
- Matrix Formula for Dot Product
- Linear Systems in Dot Product Matrix Form
- Linear Transformations
- Reflection Transformations
- Projection Transformations
- Contraction and Dilation Transformations
- Rotation Transformations
- Eigenvalues and Eigenvectors

Submit an Error: Do you think that you see an error in any of the pages? Click the link and let us know so that we can fix it as soon as possible! All help is greatly appreciated with there being so many possibilities that can be overlooked. |