Definition:Vector Subtraction/Arrow Representation
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Definition
Let $\mathbf u$ and $\mathbf v$ be vector quantities of the same physical property.
Let $\mathbf u$ and $\mathbf v$ be represented by arrows embedded in the plane such that:
- $\mathbf u$ is represented by $\vec {AB}$
- $\mathbf v$ is represented by $\vec {AC}$
that is, so that the initial point of $\mathbf v$ is identified with the initial point of $\mathbf u$.
Then their (vector) difference $\mathbf u - \mathbf v$ is represented by the arrow $\vec {CB}$.
Sources
- 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Addition and subtraction of vectors: $4$. Component and Resultant
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $3$. Addition and Subtraction of Vectors
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach