Introduction

Introduction

A line in space is completely determined once we know a point on it together with its direction -- and, equally, two distinct points on a line already fix the direction between them (the segment joining them cannot lie along any other line). This chapter uses these two basic facts to derive the equation of a line in space, in both vector and Cartesian form, and then goes on to discuss the distance of a point from a line, skew lines, and the distance between two skew or parallel lines.

Later sections extend the same position-vector approach from lines to planes: the equation of a plane through a point and perpendicular to a vector, through a point and parallel to two vectors, through three non-collinear points, in normal form, and through the intersection of two planes -- together with the angle between two planes, the angle between a line and a plane, the coplanarity of two lines, and the distance of a point from a plane.