1. Vectors Scalars Vectors Magnitude only Time, temperature, speed
Magnitude and Direction
Forces, position, velocity
Need two pieces of info to complete!

2. Forces are Vectors Two 100-lb forces act on a point
Does the total force = 200 lb?
If the forces caused the point to move, which way would it go? x y
F1 = 100 lbs
Need more information: Direction of each line
35°
F2 = 100 lbs
60°

3. Vector Addition Given two vectors, A and B Notation: R = A + B
Add vectors head to tail
B + A = A + B A R B A R B

4. Trig Laws Sum of interior angles = 180° Sine law: Cosine law: A B C  
if A = B,  = 
Cosine law:
if  = 90°, A2 = B2 + C2

5. Vector Addition x y
F1 = 100 lbs
85° a
35°
F2 = 100 lbs
60° R

6. Vector Subtraction
S = C – D = C + (-D) S C -D D

7. Vector Operations Multiplication by Scalar Direction doesn’t change
Magnitude increases
2.5A A
-0.8A

8. Resolving Vectors One vector can be broken into 2 others
FR = F1 + F2
You can find two pieces of information
Given F1, find magnitude, direction of F2
Given directions of F1,F2, find both magnitudes
Given magnitudes of F1,F2, find both directions
Draw out what you know
Use trig laws

9. Resolving Vectors Given FR and F1, find magnitude, direction of F2 F1

10. Resolving Vectors
Given FR and the directions of F1 & F2, find both magnitudes F1 F2 FR

11. Cartesian Vectors
Note that all 2-D vectors can be resolved into 2 perpendicular vectors x y
F1 = 100 lbs
35° Fy Fx

12. Adding Cartesian Vectors
Resolve all vectors into x and y components
Rx = S(All x components)
Ry = S(All y components)
R = Rx + Ry
|R| = (Rx2 + Ry2)1/2
a = tan-1(Ry/ Rx)

13. Adding Cartesian Vectorsx y
F1 = 100 lbs
F2 = 100 lbs
35°
60°