The component method is a technique for adding multiple vectors by resolving them into horizontal and vertical components, calculating their sums, and determining the resultant vector's magnitude and direction. The document outlines the steps involved in this method, including the use of the Pythagorean theorem and the arctangent function to find the angle of the resultant. A sample problem is provided to illustrate the application of the method, along with a practice exercise for further understanding.

1. COMPONEN
T METHOD

2. The component method is generally
used when more than two vectors are to
be added. The steps involved in adding
vectors using component method are as
follows:
1. Resolve the given vectors into its
horizontal and vertical components.
The components may be positive or
negative depending on which
quadratic the vector is found.

3. Signs of X and Y in the different quadrants
quadrant x y
1 + +
2 - +
3 - -
4 + -

4. The component method is generally used
when more than two vectors are to be
added. The steps involved in adding vectors
using component method are as follows.
2. Get the algebraic sum of all the
horizontal components. Get also the
algebraic sum of the vertical components.
These sums represent the horizontal
component and the vertical component of
the resultant respectively.

5. The component method is generally
used when more than two vectors are to
be added. The steps involved in adding
vectors using component method are as
follows.
3.Since the vertical and horizontal
components are perpendicular, the
magnitude of the resultant may be
calculated from the Pythagorean Theorem.
R = √(∑x)2
+(∑y)2

6. The component method is generally
used when more than two vectors are to
be added. The steps involved in adding
vectors using component method are as
follows.
4. From the signs of sum of horizontal
components and the vertical components,
determine the quadrant where the
resultant is. This will indicate the direction
of the resultant vector.

7. The component method is generally
used when more than two vectors are to
be added. The steps involved in adding
vectors using component method are as
follows.
5.
Solve for the angle the resultant
makes with the horizontal.

9. SIGNS OF X AND Y IN THE DIFFERENT
QUADRANTS
QUADRANT X Y
1 + +
2 - +
3 - -
4 + -

10. SAMPLE PROBLEM
A jogger runs 4.00 m 40o
N of E, 2.00 m east, 5.20m 30.0o
S of W, 6.50
m S, and then collapses. Find his resultant displacement from where he
starred. Solution: Let us tabulate the horizontal and vertical
components of each vector.
VECTORS HORIZONTAL
COMPONENT
VERTICAL COMPONENT
A = 4.00 m 40.0O
N
of E
+4.00 m cos 40.0o
= +
3.06 m
+ 4.00 m sin 40.0o
=2.57m
B = 2.00 m E + 2.00 m 0.00
C = 5.20 m 30.0o
S of
W
-5.20 m cos 30.0o
= -
4.50 m
-5.20 m sin 30.0o
= -
2.60 m
D = 6.50 m S 0.00 -6.50 m
∑ = +0.560 m ∑ = -6.53m

11. Solving the magnitude of the resultant R,
R = √(∑x)2
+ (∑y)2
R = √(0.56m)2
+ (-6.53m)2
= 6.55m
Θ = arctan ∑y
∑x
= arctan - 6.53
0.56
=
85.1o

12. Since ∑x is positive and ∑y is negative, the
resultant must be in the fourth quadrant ,
hence the direction must be 85.1o
S of E.
Thus R is 6.55 m 85.1o
S of E

13. Practice Exercise
Find the resultant of the following forces
by component method. F1 = 12N,south, F2
= 24N, 30o
north of west and F3 = 15 N,
75o
south of west, and F4 = 32N, 50o
south of east