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

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

## Definition

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 $x$-axis in the positive direction.

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