Chapter 29

Vectors

29.1 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 by an external force
will respond to that force by moving in the line of
the force. However, if two or more forces act simul-
taneously, 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 how
finding the resultant of two or more vectors has many
uses in engineering. (Resultant means the single vector
which would have the same effect as the individualvec-
tors.) Relative velocities and vectori,j,knotation are
also briefly explained.

29.2 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, temper-
ature and mass are entirely defined by a numerical value
and are calledscalarsorscalar quantities.
Not all quantities are like this. Some are defined
by more than just size; some also have direction. For
example, the velocity of a car may be 90km/h due
west, a force of 20N may act vertically downwards,
or an acceleration of 10m/s^2 may act at 50◦to the
horizontal.
Quantities such as velocity, force andacceleration,
whichhave both a magnitude and a direction,are
calledvectors.

Now try the following Practice Exercise

PracticeExercise 113 Scalar and vector

quantities (answers on page 352)

1. State the difference between scalar and vector
   quantities.
   In problems 2 to 9, state whether the quantities
   given are scalar or vector.


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

29.3 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.

An arrow is used to denote the sense, or direction, of the

vector.

The arrow end of a vector is called the ‘nose’ and the

other end the ‘tail’. For example, a force of 9N acting

DOI: 10.1016/B978-1-85617-697-2.00029-6