Category:Definitions/Vector Subtraction
This category contains definitions related to Vector Subtraction.
Related results can be found in Category:Vector Subtraction.
Let $\struct {F, +_F, \times_F}$ be a field.
Let $\struct {G, +_G}$ be an abelian group.
Let $V := \struct {G, +_G, \circ}_R$ be the corresponding vector space over $F$.
Let $\mathbf x$ and $\mathbf y$ be vectors of $V$.
Then the operation of (vector) subtraction on $\mathbf x$ and $\mathbf y$ is defined as:
- $\mathbf x - \mathbf y := \mathbf x + \paren {-\mathbf y}$
where $-\mathbf y$ is the negative of $\mathbf y$.
The $+$ on the right hand side is vector addition.
Arrow Representation
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 $\vec {CB}$.
Pages in category "Definitions/Vector Subtraction"
The following 2 pages are in this category, out of 2 total.