Definition:Vector Quantity/Arrow Representation
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A vector quantity $\mathbf v$ is often represented diagramatically in the form of an arrow such that:
- its length is proportional to the magnitude of $\mathbf v$
- its direction corresponds to the direction of $\mathbf v$.
The head of the arrow then indicates the positive sense of the direction of $\mathbf v$.
It can be rendered on the page like so:
It is important to note that a vector quantity, when represented in this form, is not in general fixed in space.
All that is being indicated using such a notation is its magnitude and direction, and not, in general, a point at which it acts.
- 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $2$. Length vectors
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $2$. Graphical Representation of Vectors
- 1957: D.E. Rutherford: Vector Methods (9th ed.) ... (previous) ... (next): Chapter $\text I$: Vector Algebra: $\S 1$.
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 22$: Vectors and Scalars
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $7$: Vector Spaces: $\S 32$. Definition of a Vector Space
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach