Vector Algebra

Let me first give you some brief introduction to Vector Algebra.

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 quantities, namely, scalar quantities such as length, mass, 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.

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)).

Fig 10.1

Now observe that if we restrict the line l to the line segment AB, then a magnitude
is prescribed on the line l with one of the two directions, so that we obtain a directed
line segment (Fig 10.1(iii)). Thus, a directed line segment has magnitude as well as
direction.