# Definition:Axial Vector

## 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 known as

An **axial vector** is also known as a **pseudovector**.

## Examples

### Angular Velocity

**Angular velocity** is an **axial vector**.

### Angular Acceleration

**Angular acceleration** is an **axial vector**.

## Also see

## 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