NCERT Book Class 12 Maths Chapter 10 Vector Algebra

338 MATHEMATICS

Chapter 10
VECTOR ALGEBRA

v In most sciences one generation tears down what another has built and what
one has established another undoes. In Mathematics alone each generation
builds a new story to the old structure. – HERMAN HANKEL v

10.1 Introduction
In our day to day life, we come across many queries such
as – What is your height? How should a football player hit
the ball to give a pass to another player of his team? Observe
that a possible answer to the first query may be 1.6 meters,
a quantity that involves only one value (magnitude) which
is a real number. Such quantities are called scalars.
However, an answer to the second query is a quantity (called
force) which involves muscular strength (magnitude) and
direction (in which another player is positioned). Such
quantities are called vectors. In mathematics, physics and
engineering, we frequently come across with both types of
W.R. Hamilton
quantities, namely, scalar quantities such as length, mass,
(1805-1865)
time, distance, speed, area, volume, temperature, work,
money, voltage, density, resistance etc. and vector quantities like displacement, velocity,
acceleration, force, weight, momentum, electric field intensity etc.
In this chapter, we will study some of the basic concepts about vectors, various
operations on vectors, and their algebraic and geometric properties. These two type of
properties, when considered together give a full realisation to the concept of vectors,
and lead to their vital applicability in various areas as mentioned above.
10.2 Some Basic Concepts
Let ‘l’ be any straight line in plane or three dimensional space. This line can be given
two directions by means of arrowheads. A line with one of these directions prescribed
is called a directed line (Fig 10.1 (i), (ii)).