Kerala State Board New Syllabus Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry.

## Kerala Plus One Maths Notes Chapter 12 Introduction to Three Dimensional Geometry

Introduction

To refer to a point in space we require a third axis (say z-axis) which leads to the concept of three-dimensional geometry. In this chapter, we study the basic concept of geometry in three-dimensional space.

I. Octant

Consider three mutually perpendicular planes meet at a point O. Let these three planes intercept along three lines XOX’, YOY’ and ZOZ’ called the x-axis, y-axis, and z-axis respectively. These three planes divide the entire space into 8 compartments called Octants. These octants could be named as XOYZ, XOYZ’, XOYZ, X’OYZ, XOY’Z’, X’OYZ, X’OYZ’, X’OYZ’.

Distance between two points: The distance between the points (x1, y1, z1) and (x2, y2, z2) is

Section formula:

1. Internal: The coordinate of the point R which divides the line segment joining the points (x1, y1, z1) and (x2, y2, z2) internally in the ratio l : m is

2. External: The coordinate of the point R which divides the line segment joining the points (x1, y1, z1) and (x2, y2, z2) externally in the ratio l : m is

3. Midpoint: The coordinate of the point R which is the midpoint of the line segment joining the points (x1, y1, z1) and (x2, y2, z2) is

4. Centroid: The coordinate of the centroid of a triangle whose vertices are given by the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) is