NCERT Book Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry

208 MATHEMATICS

Chapter 11

INTRODUCTION TO THREE
DIMENSIONAL GEOMETRY

vMathematics is both the queen and the hand-maiden of
all sciences – E.T. BELLv

11.1 Introduction
You may recall that to locate the position of a point in a
plane, we need two intersecting mutually perpendicular lines
in the plane. These lines are called the coordinate axes
and the two numbers are called the coordinates of the
point with respect to the axes. In actual life, we do not
have to deal with points lying in a plane only. For example,
consider the position of a ball thrown in space at different
points of time or the position of an aeroplane as it flies
from one place to another at different times during its flight.
Similarly, if we were to locate the position of the Leonhard Euler
lowest tip of an electric bulb hanging from the ceiling of a (1707-1783)
room or the position of the central tip of the ceiling fan in a room, we will not only
require the perpendicular distances of the point to be located from two perpendicular
walls of the room but also the height of the point from the floor of the room. Therefore,
we need not only two but three numbers representing the perpendicular distances of
the point from three mutually perpendicular planes, namely the floor of the room and
two adjacent walls of the room. The three numbers representing the three distances
are called the coordinates of the point with reference to the three coordinate
planes. So, a point in space has three coordinates. In this Chapter, we shall study the
basic concepts of geometry in three dimensional space.*

* For various activities in three dimensional geometry one may refer to the Book, “A Hand Book for
designing Mathematics Laboratory in Schools”, NCERT, 2005.