Vectors
COMPONENT ADDITION METHOD
Rev. 0
Page 21
CP-02
3.
Mathematically combine all y-axis components (+y at 270 = -y at 90 ).
o
o
4.
Resulting (x,y) components are the (x,y) components of the resulting vector.
The following examples illustrate vector addition using the component addition method.
Example 1:
Given the following vectors what are the coordinates of the resultant vector, that is, the sum of the
vectors?
F = (4,10), F = (-6,4), F = (2,-4), and F = (10,-2)
1
2
3
4
Step 1.
Determine the x- and y-axes components of all four original vectors.
x-axes components = 4, -6, 2, 10
y-axes components = 10, 4, -4, -2
Step 2.
Mathematically combine all x-axis components.
F = 4 + (-6) + 2 + 10
x
F = 4 - 6 + 2 + 10
x
F = 10
x
Step 3.
Mathematically combine all y-axis components.
F = 10 + 4 + (-4) + (-2)
y
F = 10 + 4 - 4 - 2
y
F = 8
y
Step 4.
Express the resultant vector.
The resultant components from the previous additions are the coordinates of the
resultant, that is, F = (10,8).
R
Example 2:
Determine the resultant, F .
R
Given:
F = 30 lbf at 0 , 10 lbf at 90
1
o
o
F = 50 lbf at 0 , 50 lbf at 90
2
o
o
F = 45 lbf at 180 , 30 lbf at 90
3
o
o
F = 15 lbf at 0 , 50 lbf at 270
4
o
o
