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 by an 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 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 individual vectors.)
Relative velocities and vector i, j , k notation are also
briefly explained.
24.2 Scalars and vectors
The time taken to fill a water tank may be measured as,
say, 50 s. Similarly, the temperature in a room may be
measured as, say, 16 ◦ C, or the mass of a bearing may
be measured as, say, 3 kg.
Quantities such as time, temperature and mass are
entirely defined by a numerical value and are called
scalars or scalar 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 is 90 km/h due west, or a force
of 20 N acts vertically downwards, or an acceleration of
10 m/s
2 acts at 50 ◦ to the horizontal.
Quantities such as velocity, force and acceleration,
which have both a magnitude and a direction, are
called vectors.
Now try the following exercise
Exercise 102 Further problems on scalar
and vector quantities
1. State the difference between scalar and vector
quantities.
In problems 2 to 9, state whether the quantities given are scalar (S) or vector (V) – answers
below.
2. A temperature of 70 ◦ C
3. 5 m 3 volume
4. A downward force of 20 N
5. 500 J of work
6. 30 cm 2 area
7. A south-westerly wind of 10 knots
8. 50 m distance
9. An acceleration of 15 m/s 2 at 60 ◦ to the
horizontal
[Answers: 2. S 3. S 4. V 5. S 6. S 7. V
8. S 9. V]
24.3 Drawing a vector
A vector quantity can be represented graphically by a
line, drawn so that:
(a) the length of the line denotes the magnitude of the
quantity, and
(b) the direction of the line denotes the direction in
which the vector quantity acts.
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 by an 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 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 individual vectors.)
Relative velocities and vector i, j , k notation are also
briefly explained.
24.2 Scalars and vectors
The time taken to fill a water tank may be measured as,
say, 50 s. Similarly, the temperature in a room may be
measured as, say, 16 ◦ C, or the mass of a bearing may
be measured as, say, 3 kg.
Quantities such as time, temperature and mass are
entirely defined by a numerical value and are called
scalars or scalar 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 is 90 km/h due west, or a force
of 20 N acts vertically downwards, or an acceleration of
10 m/s
2 acts at 50 ◦ to the horizontal.
Quantities such as velocity, force and acceleration,
which have both a magnitude and a direction, are
called vectors.
Now try the following exercise
Exercise 102 Further problems on scalar
and vector quantities
1. State the difference between scalar and vector
quantities.
In problems 2 to 9, state whether the quantities given are scalar (S) or vector (V) – answers
below.
2. A temperature of 70 ◦ C
3. 5 m 3 volume
4. A downward force of 20 N
5. 500 J of work
6. 30 cm 2 area
7. A south-westerly wind of 10 knots
8. 50 m distance
9. An acceleration of 15 m/s 2 at 60 ◦ to the
horizontal
[Answers: 2. S 3. S 4. V 5. S 6. S 7. V
8. S 9. V]
24.3 Drawing a vector
A vector quantity can be represented graphically by a
line, drawn so that:
(a) the length of the line denotes the magnitude of the
quantity, and
(b) the direction of the line denotes the direction in
which the vector quantity acts.