Analytical Geometry

Chapter 13

Straight Line

13.1  INTRODUCTION

The intersection of two planes P₁ and P₂ is the locus of all the common points on both the planes P₁ and P₂. This locus is a straight line. Any given line can be uniquely determined by any of the two planes containing the line. Thus, a line can be regarded as the locus of the common points of two intersecting planes.

Let us consider the two planes

Any set of coordinates (x, y, z) which satisfy these two equations simultaneously will represent a point on the line of intersection of these two planes. Hence these two equations taken together will represent a straight line. It can be noted that the equation ...