negative of a vectorNegativeOfAVector2026-08-20 03:18:112026-08-20 03:18:11Definition% this is the default PhysicsLibrary preamble. as your knowledge
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% define commands here\section*{Negative of a Vector}
The negative of a vector $\mathbf{u}$ is the vector with the same magnitude and
opposite direction:
\[
-\mathbf{u}.
\]
It is characterized by
\[
\mathbf{u}+(-\mathbf{u})=\mathbf 0.
\]
For directed segments,
\[
-\overrightarrow{AB}=\overrightarrow{BA},
\qquad
-(-\overrightarrow{AB})=\overrightarrow{AB}.
\]
The zero vector $\mathbf 0$ has zero magnitude and acts as the additive identity:
\[
\mathbf{u}+\mathbf 0=\mathbf{u}.
\]
\section*{Modern notation references}
The notation and terminology in this modernized article follow standard
present-day mechanics and vector-analysis usage, particularly:
\begin{enumerate}
\item J. R. Taylor, \emph{Classical Mechanics}, University Science Books, 2005.
\item D. Kleppner and R. Kolenkow, \emph{An Introduction to Mechanics}, 2nd ed., Cambridge University Press, 2014.
\item H. Goldstein, C. Poole, and J. Safko, \emph{Classical Mechanics}, 3rd ed., Addison--Wesley, 2002.
\end{enumerate}
\section*{Source}
This article is a modernized restatement of the corresponding Public Domain article in
Louis Brand, \emph{Vectorial Mechanics}, John Wiley \& Sons, New York, 1930,
Chapter I, ``Vector Algebra.'' The original 1930 edition is the source basis.