1. Characteristics, Properties & Mathematical Functions
Vector Basics
Characteristics, Properties & Mathematical Functions

2. What is a Vector? Any value that requires a magnitude and direction.
Examples we have already used this year
Velocity
Displacement
Acceleration
New example
Force: a push or pull on an object
unit: Newton (N)

3. How to show a Vector? Drawn as an arrow
Length represents the magnitude of the vector.
Arrow points in the correct direction.
Individual vectors are called COMPONENTS
The sum of 2 or more vectors is called a RESULTANT. (A resultant is one vector that represents all the components combined.)

4. Representing Direction
Draw the arrow pointing in the correct direction.
North
North is up
South is down
East is right
West is left
West
East
South

5. Vector in One Dimension
So far we have only dealt with vectors on the same plane.
Walk 10m to the right and then 5 m more to the right =
10 m +
5 m
15 m
When 2 vectors are in the same direction add the values and keep the same direction!

6. Vector in One Dimension
Walk 10m to the right and then 5 m to the left -
5 m =
10 m
5 m
When 2 vectors are in opposite directions subtract the values and keep the direction of the bigger value.

7. Between the basic directions
If your vector is exactly between 2 basics directions both will be named.
Northeast
Southeast
Northwest
Southwest N W E S

8. Direction not exactly between
Start pointing toward the last written direction.
Turn the number of degrees given toward the 1st written direction.
For example: 30˚ north of west
Start west
and turn 30˚to north N W E S

9. Direction not exactly between
Start pointing toward the last written direction.
Turn the number of degrees given toward the 1st written direction.
For example: 55˚ south of east
Start east
and turn 55˚to south N W E S

10. = Vectors in 2 Dimensions +
Vectors that are in two different directions that meet at a 900 angle to each other requires the use of Pythagorean theorem and trigonometric functions.
5 m +
4 m =
53° N of E
3 m

11. a2+b2=c2 SOH CAH TOA Sin A = a/c Cos A =b/c Tan A = a/b
Right Triangles
a2+b2=c2
SOH CAH TOA
Sin A = a/c
Cos A =b/c
Tan A = a/b

12. (3m)2 + (4m)2 =R2 R = 5m Tan θ= 4m/3m Tan-1(4/3) θ=53°N of E
Pythagorean Theorem
(3m)2 + (4m)2 =R2
R = 5m
Tan θ= 4m/3m
Tan-1(4/3)
θ=53°N of E