The Coordinate Geometry of Three-dimensional Space
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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