Advanced Engineering Mathematics, 7th Edition

7.5 Lines and Planes in 3-Space

INTRODUCTION

In this section we discuss how to find various equations of lines and planes in 3-space.

Lines: Vector Equation

As in the plane, any two distinct points in 3-space determine only one line between them. To find an equation of the line through P₁(x₁, y₁, z₁) and P₂(x₂, y₂, z₂), let us assume that P(x, y, z) is any point on the line. In FIGURE 7.5.1, if r = , r₁ = , and r₂ = , we see that vector a =