Chapter 12



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.


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(x1, y1, z1) and Q(x2, y2, z2) be two points ...

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