Chapter 24

Vectors

24.1 Introduction

This chapter initially explains the difference between
scalar and vector quantities and shows how a vector is
drawn and represented.
Any object that is acted upon byan external force will
respond to that force by moving in the line of the force.
However, if two or more forces act simultaneously, the
result is more difficult to predict; the ability to add two
or more vectors then becomes important.
This chapter thus shows how vectors are added and
subtracted,both by drawing and by calculation,and find-
ingthe resultant of twoor more vectors has many uses in
engineering. (Resultant means the single vector which
would have the same effect as the individual vectors.)
Relative velocities and vectori,j,knotation are also
briefly explained.

24.2 Scalars and vectors

The time taken to fill a water tank may be measured as,
say, 50s. Similarly, the temperature in a room may be
measured as, say, 16◦C, or the mass of a bearing may
be measured as, say, 3kg.
Quantities such as time, temperature and mass are
entirely defined by a numerical value and are called
scalarsorscalar quantities.
Not all quantities are like this. Some are defined by
more than just size; some also have direction. For exam-
ple, the velocity of a car is 90 km/h due west, or a force
of 20N acts vertically downwards, or an acceleration of
10m/s^2 acts at 50◦to the horizontal.
Quantities such as velocity, force andacceleration,
whichhave both a magnitude and a direction,are
calledvectors.

Now try the following exercise

Exercise 102 Further problemson scalar

and vector quantities

1. State the difference between scalar and vector
   quantities.
   In problems 2 to 9, state whether the quanti-
   ties given are scalar (S) or vector (V) – answers
   below.


2. A temperature of 70◦C


3. 5m^3 volume


4. A downward force of 20N


5. 500J of work


6. 30cm^2 area


7. A south-westerly wind of 10knots


8. 50m distance


9. An acceleration of 15m/s^2 at 60◦ to the
   horizontal
   [Answers: 2. S 3. S 4. V 5. S 6. S 7. V


10. S 9. V]

24.3 Drawing a vector

A vector quantity can be represented graphically by a

line, drawn so that:

(a) thelengthof the line denotes the magnitude of the

quantity, and

(b) thedirectionof the line denotes the direction in

which the vector quantity acts.