Scalar Component and Projection on an Axis
Let ê be a unit vector defining the positive direction of an axis. The scalar component of u along
the axis is
where 𝜃 is the angle from the positive axis to u.
The corresponding vector projection is
After the dot product is introduced, these become
Figure 10, modernized: signed scalar components of vectors on a directed axis.
Projection is linear:
Modern notation references
The notation and terminology in this modernized article follow standard present-day mechanics
and vector-analysis usage, particularly:
- J. R. Taylor, Classical Mechanics, University Science Books, 2005.
- D. Kleppner and R. Kolenkow, An Introduction to Mechanics, 2nd ed., Cambridge
University Press, 2014.
- 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 Domain article in Louis
Brand, Vectorial Mechanics, John Wiley & Sons, New York, 1930, Chapter I, “Vector Algebra.”
The original 1930 edition is the source basis.
