Introduction to vector, for Malaysian Polytechnic's students. Especially for IT courses

1. 1

2. 2
Understand vector quantities
• State the two components of
a vector.
• Draw a directed line to
represent a vector.

3.  Quantities such as time, temperature
and mass are entirely defined by a
numerical value and are called scalars
or scalar quantities.
› E.g. temperature in a room is 16 C.
 Quantities such as velocity, force and
acceleration, which have both a
magnitude and a direction, are called
vectors.
› E.g. the velocity of a car is 90km/h due west.
3

4. 
4

5.  A vector quantity can be represented
graphically by a line, drawn so that:
› the length of the line denotes the magnitude
of the quantity, and
› the direction of 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’.
5

6.  For example, a force of 9N acting at 45◦
to the horizontal is shown in Fig. 1. Note
that an angle of +45◦ is drawn from the
horizontal and moves anticlockwise.
Fig. 1
6

7.  A velocity of 20m/s at −60◦ is shown in
Fig. 2. Note that an angle of −60◦ is
drawn from the horizontal and moves
clockwise.
Fig. 2
7

8. 
8

9. 9
Solve addition vectors:
• Determine the resultant
vector using graphical
method:
i) triangle method,
ii) parallelogram method.

10.  Adding two or more vectors by drawing
assumes that a ruler, pencil and
protractor are available.
 Results obtained by drawing are
naturally not as accurate as those
obtained by calculation.
10

11.  Triangle @ Nose-to-tail method
› Two force vectors, F1 and F2, are shown in
Fig. 3.
› When an object is subjected to more than
one force, the resultant of the forces is found
by the addition of vectors.
Fig. 3
11

12.  To add forces F1 and F2:
› Force F1 is drawn to scale horizontally, shown
as Oa in Fig. 4.
› From the nose of F1, force F2 is drawn at
angle θ to the horizontal, shown as ab.
› The resultant force is given by length Ob,
which may be measured.
 This procedure is called the ‘nose-to-tail’
or ‘triangle’ method.
12

13. a
b
0
Fig. 4
Fig. 3
13

14.  Parallelogram method
› To add the two force vectors, F1 and F2, of Fig.
3:
› A line cb is constructed which is parallel to and
equal in length to Oa (see Fig. 5).
› A line ab is constructed which is parallel to and
equal in length to Oc.
› The resultant force is given by the diagonal of
the parallelogram, i.e. length Ob.
 This procedure is called the
‘parallelogram’ method.
14

15. a
b
0
Fig. 5
Fig. 3
c
15

16.  A force of 5N is inclined at an angle of 45◦ to
a second force of 8 N, both forces acting at
a point. Find the magnitude of the resultant
of these two forces and the direction of the
resultant with respect to the 8N force by:
› (a) the ‘nose-to-tail’method, and
› (b) the ‘parallelogram’ method.
Answer:
12N at
(approximately)
17˚ from
horizontal
16

17. Answer:
18N at
(approximately)
34˚ from
horizontal
17

18. Answer:
22m/s at
(approximately)
105˚ from
horizontal
18

19. 19

20. Prepare for Quiz 1 and Peer
Assessment 1, for next class!
20