Download Section 2.2

Objective:
Find the components of a vector.
 Number plane, or Cartesian
coordinate system – a plane
determined by the
horizontal line called the xaxis and a vertical line
called the y-axis
intersecting at right angles.
 Plane divided in two four
quadrants: I, II, III, and IV.
 Vector drawings
 A directed line segment; arrowhead indicates direction
 Length indicates magnitude
 Starts with initial point
 Ends with terminal point, or end point
R
 The sum of two or more vectors is called the resultant
vector.
 When two or more vectors are added are added, each
vector is called a component vector.
 Useful component vectors are the components that are
both perpendicular and that are parallel to the x- and
y-axes.
 The horizontal component is called the x-component.
 The vertical component is called the y-component.
R
Ry
Rx
 The x- and y-components can be expressed as signed
numbers.
 Absolute value indicates magnitude of vector.
 The sign indicates the direction.
x-component
y-component
+, if right
+, if up
-, if left
-, if down
Find the x- and y-components of vector R.
R
Find the x- and y-components of vector v.
v
Find the x- and y-components of vector u.
u
 We can find the resultant of several vectors using
arithmetic graphing.
 The sum of all x-components for each vector gives the x-
component for the resultant vector, Rx.
 The sum of all y-components for each vector gives the ycomponent for the resultant vector, Ry.
R
A
Ax = +3
B
By = +4
By = +2
Ay = +2
Vector
x-comp
y-comp
A
+3
+2
B
+2
+4
R
+5
+6
Given vectors A, B, and C, graph and find the x- and ycomponents of the resultant vector R.
Vector
A
C
B
B
C
R
A
x-comp
y-comp
 Two vectors are equal when they have the same
magnitude and the same direction.
 They are opposites or negatives of each other when
they have the same magnitude but opposite direction
 A vector may be placed in any position in the number
plane as long as its magnitude and direction are not
changed.
To add two or more vector graphically:
1. Draw first vector with initial point at origin
2. The second vector should be drawn with its initial
point on the on the end point of first vector
3. If there are more vectors repeat until the last one
drawn.
4. The sum, or the resultant vector, is drawn by joining
the initial point of the first vector to the end point of
the last vector.
Note: the order in which the vector are added does not
matter.
Given vectors A, B, and C, graph and find the x- and ycomponents of the resultant vector R.
B
A
B
A
R
C
C
Rx = +1
Ry = -5