Definition:Orientation of Coordinate Axes/Cartesian 3-Space

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This page is about orientation of Cartesian 3-space in the context of analytic geometry. For other uses, see Orientation.

Definition

There are $2$ different orientations of a Cartesian $3$-space:


Right-hand-3-space.png $\qquad \qquad \qquad$ Left-hand-3-space.png


Right-Handed

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.


Right-hand-3-space.png


Left-Handed

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

Let a left 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.


Left-hand-3-space.png


Also known as

The orientation of a Cartesian coordinate system is known as its handedness.

The term arises from whether it is defined as a left-handed system or a right-handed system.


Sources

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