7.2 Vectors in 3-Space

INTRODUCTION

In the plane, or 2-space, one way of describing the position of a point P is to assign to it coordinates relative to two mutually orthogonal, or perpendicular, axes called the x- and y-axes. If P is the point of intersection of the line x = a (perpendicular to the x-axis) and the line y = b (perpendicular to the y-axis), then the ordered pair (a, b) is said to be the rectangular or Cartesian coordinates of the point. See FIGURE 7.2.1. In this section we extend the notions of Cartesian coordinates and vectors to three dimensions.

A point P is marked on quadrant 1 of a coordinate plane. A vertical line from P intersects the x axis at a distance a from the origin. A horizontal line from P intersects the y axis at a distance b from the origin. The coordinates of P are (a, b).

FIGURE 7.2.1 Rectangular coordinates in 2-space

Rectangular Coordinate System ...

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