### Vector Addition and Subtraction

```Vector Addition
and
Subtraction
Do Now
Differentiate between a vector
and scalar
 Give an example of each

Parallel Vectors
Add like numbers on a number line.
5
8
5 + 8 = 13
5
8
8-5=3
Perpendicular Vectors
Use Pythagorean’s Theorem to
determine the magnitude
Use Tangent to determine the
direction
Example
A person walks 40 m north and then 30
m east. What is their displacement?
b
a
a2 + b2 = c2
302 + 402 = c2
c = 50m
tan  = opp/adj
= tan–1 (b/a)
Graphical Method
Assign a scale to the vectors
ex. 1N in problem = 1cm in diagram
Draw vectors head to tail using a
protractor to determine direction and
a ruler to determine magnitude.
Draw the resultant vector. Measure its
magnitude with a ruler and its
direction with a protractor
Parallelogram Rule
When two vectors have a tail at the
same place, they may be added
together by moving the tail of one
to the head of the other using a
parallelogram.
b
b
ad = ab + bd
d
a
a
c
c
Sample Problem
Solve Graphically and Algebraically
A plane flies with a velocity of 52 m/s
east through a 12 m/s cross wind
blowing the plane south. Find the
magnitude and direction (relative to due
east) of the resultant velocity at which it
travels.
 An ambitious hiker walks 25 km west
and then 35 km south in a day. Find the
magnitude and direction (relative to due
west) of the hiker's resultant
displacement.

Adding Vectors that are not
Perpendicular
Select a coordinate system.
Draw and label vectors
Find the x and y components of all
vectors using trigonometric functions
SohCahToa
Use Pythagorean Theorem to find the
magnitude of the resultant vector.
Use trigonometric function to find the
angle of the resultant vector.
```