Chapter 3.2 – Drawing Vectors
Adding Vectors
 The process of adding vectors has also
been previously discussed in our section of
Newton’s Laws.
 The net force was the result ( or resultant) of
adding up all the force vectors.
 In that chapter, the rules for adding vectors
were kept simple.
Practice: Find the Resultant
(Net Force)
 In this chapter, the
task of adding
vectors will be
extended to more
complicated cases in
which the vectors are
directed in directions
other than purely
vertical and
horizontal directions.
 There are a
variety of
methods for
determining the
magnitude and
direction of the
result of adding
two or more
vectors.
 The 2 Methods that
we will learn how to
use:
 1. Pythagorean
Theorem (using Trig)
 2. Head – to – Tail
Method ( using
graphs)
Calculating Resultants Using the
“Head – To – Tail” Method
1. Add the vectors by first attaching them head to tail.
2. Once all the vectors have been added head-to-tail,
the resultant is then drawn from the tail of the first vector
to the head of the last vector; i.e., from start to finish
3. Once the resultant is drawn, its length can be
measured and converted to real units using the given
scale.
4. The direction of the resultant can be determined by
using a protractor and measuring its counterclockwise
angle from the horizon.
EXAMPLE #1 Add the following
vectors together and find the
resultant
 20 m, 45 deg. + 25 m,
300 deg. + 15 m, 210
deg.
 Scale: 1 cm = 5m
Step #2
 Draw your vectors
“Head – to- Tail”
 Draw the resultant in
red.
 Draw the resultant
from the start to
finish.
 The order in which
you draw or
attach) your
vectors doesn’t
matter, as long as
your don’t change
the magnitude or
the direction.