Definition:Axial Vector/Definition 1
Definition
An axial vector is a vector quantity $\mathbf V$ used to specify action which takes place around an axis of rotation.
In this case, the $\mathbf V$ is considered as acting parallel to the axis about which $\mathbf V$ acts.
As for a polar vector, the length of $\mathbf V$ indicates the magnitude of $\mathbf V$.
The direction of $\mathbf V$ is determined by convention to be according to the right-hand rule.
Right-Hand Rule
Let $\mathbf V$ be an axial vector acting with respect to an axis of rotation $R$.
Consider a right hand with its fingers curled round $R$ so that the fingers are pointed in the direction of rotation of $\mathbf V$ around $R$.
The right-hand rule is the convention that the direction of $\mathbf V$ is the direction in which the thumb is pointing:
Also see
- Results about axial vectors can be found here.
Sources
- 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