1. Chapter 4
Vectors

2. 4.1 Properties of Vectors Representing Vector Quantities
Graphical Representation
Algebraic Representation
The Resultant Vector
Graphical Addition of Vectors
Tip to Tail
Magnitude of the resultant
Law of Cosines
R2 = A2 + B2 – 2ABcosΘ

3. Subtracting Vectors Relative Velocities a – b = a + (-b)
Just reverse the direction of the subtracted vector and then add.
Relative Velocities
Pick your point of reference a -b c b

5. 4.2 Components of Vectors Choosing a Coordinate System Components
After picking a coordinate system, any vector can then be described from that reference.
Components
Each vector can be broken down into x- and y- components.
Algebraic Addition of Vectors
Add the components in each direction then re-assemble into the resultant.
Find the direction using Tan Θ = Ry/Rx

10. PSS Determine if you will be solving graphically or algebraically.
Break all vectors into components
Set up a table
Add each component direction together paying attention to any negative signs.
Find the magnitude of the resultant using Pythagorean theorem.

11. 6. Find the angle the resultant makes using Tan Θ = Ry/Rx Rearrange this to solve for Θ.
This equation is used to find the angle the resultant makes with Rx. Report the angle for the resultant as measured from the positive X-axis.
7. Check your answer. A vector has both magnitude and direction!