Vectors
What is a vector
quantity?
Vectors
Vectors are quantities
that possess magnitude
and direction.
»Force
»Velocity
»Acceleration
What are scalar quantities?
Scalars
• Scalars are quantities that possess
only magnitude.
•
•
•
•
•
•
•
How much money you have
How old you are
How tall you are
Temperature
Pounds
Speed
Length
Represent the following
vectors
• A wind velocity of 20 mph due north
• A boat traveling 4 knots per hour heading
east
• A car traveling 60 mph heading south
Equal Vectors
• Same length
• Same direction
Parallel Vectors
Adding Vectors
Three Methods for
Adding Vectors
• Tail to Head Method
• Parallelogram Method
• Component Method
Tail to Head Method
Adding Vectors Tail to
Head
 Draw Vector A with the correct length and angle.
 Draw Vector B with the correct length and angle, but such
the Vector B’s tail starts at the head of vector A.
 The Vector C is then represented by an arrow from the tail
of Vector A to the head of Vector B.
Adding Vectors
Same direction
•
Adding Vectors
Opposite directions
Adding Vectors
Components
Parallelogram Method
Parallelogram Method
Vector 2
Vector 1
Component Method
Component Method
Find the sum of Vector 1 and Vector 2.
Vector 1 is 25 m 50 N of E
Vector 2 is 10 m 45 N of W
Component Method
• Using Trigonometry, find the x-component
and the y-component for each vector.
• Add up the x-components.
• Add up the y-components.
• Use the Pythagorean Theorem and the trig
functions to get the size and direction of
the resultant vector.
Finding the x-component
adjacent
cos  
hypotenuse
Y-component

X-component
Finding the x-component
Vector 1 is 25 m 50 N of E
adjacent
cos  
hypotenuse
x  component
o
cos 50 
25 meters
X-component = 25 * cos 50
X- component (vector 1) = 16.1 m
Y-component
50
X-component
Finding the y-component
opposite
sin  
hypotenuse
Y-component

X-component
Finding the y-component
Vector 1 is 25 m 50 N of E
y  component
sin 50 
25 meters
o
y-component = 25 * sin 50
y- component (vector 1) = 19.2 m
Y-component
50
X-component
Finding the x-component
Vector 2 is 10 m 45 N of W
adjacent
cos  
hypotenuse
Y-component
45
X-component
x  component
cos 45 
10 meters
o
X-component = 10 * cos 135
X- component (vector 2) = -7.1 m
Finding the y-component
Vector 2 is 10 m 45 N of W
opposite
sin  
hypotenuse
Y-component
45
X-component
y  component
sin 45 
10 meters
o
y-component = 10 * sin 135
y- component (vector 2) = 7.1 m
Adding the x- components
Vector 1 + Vector 2
16.1 m+ -7.1 m = 9 m
Adding the y-components
Vector 1 + Vector 2
19.2 m+ 7.1 m = 26.3 m
Using the Pythagorean
Theorem
c²= a²+ b²
c²= 9²+26.3²
c²= 772.69
c = 27.8 meters
opposite
tan  
adjacent
26.3
tan  
9
1 26.3
  tan
9
 = 71.1 N of E
Mission Impossible
Vectors on the Go
Good Luck