# The Coordinate Geometry of Three-dimensional Space

## Abstract

It is now time to enter the real world of three dimensions. In order to introduce cartesian coordinates we necessarily require three mutually perpendicular axes, labelled *x*, *y* and *z*-axes, all of which meet at a common point, the coordinate origin. There are two independent ways of placing these axes, known as left-handed and right-handed triads of axes. In both types we may place the *x* and *y*-axes as in two-dimensional space, in the plane of the page (or screen) — the positive *x* axis placed to the right of the origin and the positive *y*-axis above the origin. This just leaves the placement of the *z*-axis (whence the two classifications of triads); it may be into the page (left-handed) or out of the page (right-handed). In this book we *always* use the left-handed notation.

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