1. Vectors in 2 Dimensions
10.0m
6.0m
8.0m

2. Representation of vectors in 2D
Polar form (magnitude and direction)
ex: Dr = 10.0m 37⁰
Component form (x and y (and z) components)
ex: Dr = (8.0 i j)m
or Dr = (8m, 6m) or Dx = 8m, Dy = 6m
Graphical form (scale drawing)
ex: Dr =
10.0m
37 ⁰

3. Adding or Subtracting Vectors
Vectors can only be added or subtracted if they are in COMPONENT or GRAPHICAL forms
ADDING Graphically: Make a scale drawing
ADDING or SUBTRACTING by components:
Convert vectors from polar to component form
Add or subtract x comp., add or subtract y comp.
Convert back to polar form (if needed)

4. Converting Vectors: Polar to Comp.
Sketch the polar vector
Sketch the components (legs) X, then Y
Use trig to compute the components
Repeat as needed for other vectors
Ex: Convert 20m, 120 ⁰ to component form

5. Converting Vectors: Comp. to Polar
Draw the X then Y components (legs) TIP to TAIL
Draw the hypotenuse (magnitude of polar vector)
Compute the direction of the polar vector
Ex: Convert Dr = m i m j (Dx = m Dy = m) to polar form

6. Converting Practice Convert 20m, 120° to component form.
Convert Dr = (-15 i j)m to polar form.

7. Position & Displacement in 2D
Dr = rf-ri where rf and ri are position vectors
Drtotal = Dr1 + Dr2+…+ Drn
r = xî + yĵ + zǩ

8. Examples
Ex1: During practice, Ryan marches 10m,30° and then 10m, 150°. What is his total displacement?
Ex2: A radar station tracks a satellite that moves from 160km,28° to 100 km70°. What is the satellite’s displacement?

9. Posted Examples
p 57 # 5, 8, 11, 16, 15