1. VECTORS

2. Vectors Vectors have magnitude and direction
They are represented by an arrow-tipped line segment( )
The length (drawn to scale) represents the magnitude of the quantity
The direction of the arrow represents the direction of the quantity

3. Vectors Vector Addition in One Dimension
Add by placing the tail of one vector to the head of another:
The resultant represents the sum of the two
Resultant – vector sum of the component vectors
**order of addition of vectors does not matter**

4. Vectors Vector Addition in Two Dimensions
Place the tail of one vector to the head of another.
Draw the resultant from the tail of the FIRST vector to the head of the LAST

5. Vectors Graphical Addition of Vectors
Follow the same rules for vector addition, however, everything is drawn to scale…
Set up an appropriate scale (1cm=1m)
Draw the vectors to scale with a ruler, and use a protractor to measure the correct angle
Once the resultant is drawn, measure it with a ruler and convert using your scale.
Measure the angle of the resultant counterclockwise from 0° (east)

6. Vectors Analytical Addition of Vectors (2 vectors)
Set up the vectors head to tail
Use the Law of Cosines to find the resultant
c2 = a2 + b2 –2ab cosine C OR
Use the Law of Sines to find the resultant
sine A/a = sine B/b = sine C/c

7. Vectors Analytical Addition of Vectors continued…
If the vectors form a RIGHT triangle(90°) when placed head to tail, use the SOCATOA method and Pythagorean Theorem:
sin  = opp/hyp cos = adj/hyp
tan  = opp/adj
a2 + b2 = c2

8. Vectors Components of Vectors
You can resolve a vector triangle using the resultant and working backwards
Choose two components (sides) that are perpendicular to one another(90°)
One component is the x-component and one component is the y-component

9. Vectors Components cont. x= R cos y = R sin 
Calculate all of the x and y components
Sum all of the x components; sum all of the y components
Since x and y form a right triangle, use Pythagorean theorem to calculate the resultant…(see sheet for component method)