3.2 Vector Addition and Subtraction
1.
Vector addition can be done geometrically
with the triangle method or the
parallelogram method for two vectors
2. Vector addition can be done geometrically
with the polygon method for more than two
vectors.
3. Vector subtraction is a special case of
vector addition because
A – B = A + (-B)
where a negative vector has the same
magnitude but opposite direction of the
positive vector.
Ex: the negative vector of 45 m/s north is
45 m/s south
Geometric methods of vector addition
Triangle method:
Geometric Methods of Vector Addition
Parallelogram Method:
The parallelogram method can
be used to sum two vectors by
placing both of their tails together
and sketching the two remaining
sides that would create a
parallelogram. The diagonal with
the common tail represents the
resultant vector, whose direction
is away from the initial vector’s
common origin.
Example 3
Two displacement vectors A = 5m and
B = 3m are given. Show:
a) A + B with the triangle method
b) A + B with the parallelogram method
c) A – B with the triangle method
d) A – B with the parallelogram method
Vector addition is conveniently done by the
analytical component method (See p. 78 in text)
1. Resolve the vectors to be added into their xand y- components. Include directional signs
(positive or negative) in the components.
2. Add, algebraically, all the x-components
together and all the y-components together to
get the x- and y- components of the resultant
vector, respectively.
3. Express the resultant vector using
a) The component form, C = Cxx + Cyy or
b) The magnitude-angle form,
C = sqrt(Cx2 + Cy2), q = tan-1(Cy/Cx)
Vectors can be resolved into components and
the components added separately; then
recombine to find the resultant.
Use the analytical component method to find the
resultant velocity of the following two velocities.
V1 = 35 m/s 30o north of east
V2 = 55 m/s 45o north of west
• Resolve the vectors to be added into their
x- and y- components
• Add x-components together and y-components
together
• Express the resultant vector in component form:
• In magnitude-angle form:
Concept Test – slides 2-13
• D:\Chapter_03\Assess\Assess_Present\W
BL6_ConcepTests_Ch03.ppt
• Homework Problems: p. 96-98; 25, 27, 28,
31, 33, 43, 44, 48, 49, 53