Negative of a Vector

The negative of a vector $\mathbf{u}$ is the vector with the same magnitude and opposite direction:

$\displaystyle -\mathbf{u}.$

It is characterized by

$\displaystyle \mathbf{u}+(-\mathbf{u})=\mathbf 0.$

For directed segments,

$\displaystyle -\overrightarrow{AB}=\overrightarrow{BA}, \qquad -(-\overrightarrow{AB})=\overrightarrow{AB}.$

The zero vector $\mathbf 0$ has zero magnitude and acts as the additive identity:

$\displaystyle \mathbf{u}+\mathbf 0=\mathbf{u}.$

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.

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