summary of vector algebra

Summary of Vector Algebra

Summary of vector algebra techniques in introductory physics:

Basic operations

Linear and affine representations

If a,b are nonparallel, every vector in their plane is αa + βb. If a,b,c are noncoplanar, every vector in space is

For point division,

For weighted points,

Cartesian components

Dot product

For nonzero vectors,

Cross product

For nonzero vectors,

Triple products

whose absolute value is the parallelepiped volume, and

These identities form the working vector toolkit used throughout the remainder of Vectorial mechanics.

Modern notation references

The notation and terminology in this modernized article follow standard present-day mechanics and vector-analysis usage, particularly:

1. J. R. Taylor, Classical Mechanics, University Science Books, 2005.
2. D. Kleppner and R. Kolenkow, An Introduction to Mechanics, 2nd ed., Cambridge University Press, 2014.
3. H. Goldstein, C. Poole, and J. Safko, Classical Mechanics, 3rd ed., Addison–Wesley, 2002.

Source

This article is a modernized restatement of the corresponding Public article in Louis Brand, Vectorial Mechanics, John Wiley & Sons, New York, 1930, Chapter I, “Vector Algebra.” The original 1930 edition is the source basis.