UNIT THREE
Lesson Three: Components of Vectors
When we add or subtract two or more vectors, the result (or answer) is called the RESULTANT.
When we wish to express the LENGTH of a vector ONLY, we use absolute value bars around our vectors.
r
r
r
r
So, the length of a vector AB would be written AB . The length of a vector v would be written v .
Any vector can be expressed as a sum of its perpendicular COMPONENTS.

we can find the RESULTANT
Likewise, if we know
the perpendicular
vector.

 COMPONENTS of a vector,
Traditionally, the perpendicular components are vectors that are drawn along a horizontal and vertical line.
We usually use the x- and y-axes.
Consider the vector below with a terminal point at x, y:
r
y
r r
sin   r ,  y  v sin 
v
r
x
r r
cos  r ,  x  v cos
v

y
x, y
r
v



r
v cos

r
v sin 

x
UNIT THREE
km
N54W . Draw a diagram and find the magnitude of the horizontal and
h
vertical components (its “perpendicular” components).
Example: Bernie is driving 65
N

E
W
S
Example: Draw a vector that represents a force of 245 N acting at an angle of 25 to the horizontal. Find the
vertical and horizontal components.
hw. P.48#1,3,4,6