## Chapter 12

## Plane

##### 12.1 INTRODUCTION

In three-dimensional coordinate geometry, first we define a plane and from a plane we define a straight line. In this chapter, we define a plane and obtain its equation in different forms. We also derive formula to find the perpendicular distance from a given point to a plane. Also, we find the ratio in which a plane divides the line joining two given points.

**Definition 12.1.1:** A plane is defined to be a surface such that the line joining any two points wholly lies on the surface.

##### 12.2 GENERAL EQUATION OF A PLANE

Every first degree equation in *x*, *y* and *z* represents a plane.

Consider the first degree equation in *x*,* y* and *z* as

where *a, **b*, c and *d* are constants. Let *P*(*x*_{1},* y*_{1}, *z*_{1}) and *Q*(*x*_{2}, *y*_{2}, *z*_{2}) be two points ...