Vectors and Graphical

Vector Addition

What is a vector?

Simply put, a vector is any measurement with a direction.

A common example would be velocity. A car can travel 75

Km/hr in a Northerly direction.Other examples of vectors are as follows:·185 soldiers marching from the north·ship traveling at 22 knots to the south east·one billion dollars from Asian markets·8.5 people contracting H1N1 per day2 from the southern states·plane traveling 625 mph going South at 162 degrees

North

East

South

West

We can us the coordinate system to map out vectors.

00

900

1800

2700

We can also use the navigational degrees to make more precise measurements of position.

00

900

1800

2700

00

900

1800

2700

30 Km/hr @ 450

60 Km/hr @ 1350

60 Km/hr @ 3150

How to Add Vectors

Step #1 - From the origin, draw your first vector.

Step #2 - Place the center of your protractor on the arrow (head) of the first drawn vector. Making sure it is oriented properly (N, S, E, W), draw the second vector.

Step #3 - Continue this process until all vectors in the equation have been drawn.

Step #4 - Draw a vector from the origin to the head of the last vector drawn. This is your resultant vector. Measure the length (magnitude) and the direction (degrees) of the resultant vector.

For example, let's add vector A + B

Vector A is 5.8 cm @ 33o

Vector B is 4.6 cm @ 266o

Vector A

Vector B

Resultant Vector

How to Subtract Vectors

Subtracting vectors is similar to the process of adding them except when drawing the vector being subtracted, reverse the direction by subtracting 180 degrees from the initial direction.

e.g. A - B

Vector A is 5.8 cm @ 33o

Vector B is 4.6 cm @ 266o

When subtracting vector B from vector A, change the direction of vector B to 86o (266o-180o) which is the opposite direction.

Subtraction means the opposite direction (-180o)

For example, let's subtract vectors A - B

Vector A is 5.8 cm @ 33o

Vector B is 4.6 cm @ 266o

Vector A

Vector B

Resultant Vector

Vector Addition

17 cm6 cm

33

o

N

W E

S