# Definition:Orientation of Coordinate Axes/Cartesian 3-Space/Right-Handed

< Definition:Orientation of Coordinate Axes | Cartesian 3-Space(Redirected from Definition:Right-Handed Cartesian 3-Space)

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*This page is about Orientation in the context of Analytic Geometry. For other uses, see Orientation.*

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## Definition

A Cartesian $3$-Space is defined as being **right-handed** if it has the following property:

Let a **right hand** be placed such that:

- the thumb and index finger are at right-angles to each other
- the $3$rd finger is at right-angles to the thumb and index finger, upwards from the palm
- the thumb points along the $x$-axis in the positive direction
- the index finger points along the $y$-axis in the positive direction.

Then the $3$rd finger is pointed along the $z$-axis in the positive direction.

## Also known as

A **right-handed orientation** of a Cartesian $3$-Space is also referred to as the **positive orientation**.

Some sources refer to the $3$ coordinate axes in a **right-handed Cartesian 3-space** as a **right-handed triad**.

## Also see

## Sources

- 1921: C.E. Weatherburn:
*Elementary Vector Analysis*... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Components of a Vector: $7$. The unit vectors $\mathbf i$, $\mathbf j$, $\mathbf k$ - 1936: Richard Courant:
*Differential and Integral Calculus: Volume $\text { II }$*... (previous) ... (next): Chapter $\text I$: Preliminary Remarks on Analytical Geometry and Vector Analysis: $1$. Rectangular Co-ordinates and Vectors: $1$. Coordinate Axes - 1951: B. Hague:
*An Introduction to Vector Analysis*(5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $4$. Components of a Vector - 1964: D.E. Rutherford:
*Classical Mechanics*(3rd ed.) ... (previous) ... (next): Chapter $\text I$: Kinematics: $1$. Space and Time - 1967: D.E. Bourne and P.C. Kendall:
*Vector Analysis*... (previous) ... (next): Chapter $1$: Rectangular Cartesian Coordinates and Rotation of Axes: $1.1$ Rectangular cartesian coordinates - 1992: Frederick W. Byron, Jr. and Robert W. Fuller:
*Mathematics of Classical and Quantum Physics*... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.2$ The Resolution of a Vector into Components - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Cartesian coordinate system** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Cartesian coordinate system**