Introduction to Three Dimensional Geometry | Class 11 Mathematics Notes

11.1 Introduction

In this introductory section, the concept of extending coordinate geometry from two dimensions to three dimensions is established. In two-dimensional geometry, the position of a point in a plane is located using two mutually perpendicular lines called coordinate axes, and the point is represented by two numbers called coordinates. However, in real life, many objects and points exist in three-dimensional space rather than just on a plane. For example, the position of a ball thrown in space at different times or the position of an airplane flying from one place to another cannot be described using only two coordinates. Similarly, to locate the position of the lowest tip of an electric bulb hanging from the ceiling or the central tip of a ceiling fan in a room, we need not only the perpendicular distances from two adjacent walls but also the height from the floor. This necessitates the use of three numbers representing the perpendicular distances from three mutually perpendicular planes: the floor and two adjacent walls. These three numbers are called the coordinates of the point with respect to the three coordinate planes. Thus, a point in space is represented by three coordinates. This chapter introduces the basic concepts of geometry in three-dimensional space, laying the foundation for further study of spatial geometry and analytical geometry in three dimensions.

📊 Diagram: See figure_1: Portrait of Leonhard Euler (1707-1783), a mathematician who contributed significantly to geometry.

🧪 Activity: For various activities in three-dimensional geometry, refer to 'A Hand Book for Designing Mathematics Laboratory in Schools', NCERT, 2005.

🔗 Connection: This introduction leads to the next section where the three-dimensional coordinate system is formally defined using three coordinate axes and planes.