Understand vector quantities
• State the two components of
• Draw a directed line to
represent a vector.
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
› E.g. the velocity of a car is 90km/h due west.
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’.
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.
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
Solve addition vectors:
• Determine the resultant
vector using graphical
i) triangle method,
ii) parallelogram method.
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.
Triangle @ Nose-to-tail method
› Two force vectors, F1 and F2, are shown in
› When an object is subjected to more than
one force, the resultant of the forces is found
by the addition of vectors.
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.
› To add the two force vectors, F1 and F2, of Fig.
› 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
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.