1. Introduction to Vectors
Chapter 3 section 1

2. Scalar Quantity
Scalar – A quantity that can be completely specified by its magnitude, but NO direction.
Examples:
Speed
Distance
Volume
Energy
Time
Mass

3. Vector Quantity
Vector – A quantity that can be described by its magnitude AND its direction.
Examples:
Displacement
Velocity
Acceleration
Force
Momentum

4. Vectors and Scalars in the Book
Vectors quantities are indicated in Boldface by their variable.
v = 30 m/s
Scalars quantities are indicated in italics by their variable.
t = 3.2 s

5. Vector Diagrams
In diagrams, vectors are shown as arrows that point the direction of its magnitude.
Length of arrow: Magnitude of the vector
Direction of arrow: Path of vector
v = 30 mi/hr
v = 60 mi/hr

6. Resultant
Resultant – A vector representing the sum of two or more vectors.
When adding vectors, they must have the same units and describe similar quantities.
Example:
The sum of the vectors must all be velocity and must be in units of m/s.

7. Vector Addition in 1-Dimension
A=5m
B=2m
R=7m
A+B=R
5m + 2m = 7m
A=5m
B=3m
R=2m
A+B=R
5m + (-3m) = 2m

8. Head-to-Tail Method
To add two (or more) vectors together graphically using the head-to-tail method you simply draw the first vector and then draw the second vector with its tail at the head of the first vector.
If there are more vectors to be added draw each one with its tail at the head of the preceding one. The sum or resultant is a vector drawn from the tail of the first vector to the head of the last vector. It does not matter in which order you add them.

9. Vectors
The resultant always measures from where you started to where you end at.
TAIL
HEAD

10. Cartesian Plane
90°
180° 0°
270°

11. Vector Angles
When describing the direction of a vector, the angle always starts at the 0 degrees on the x-axis and moves counter-clockwise to reference the direction of the vector.
θ=300°
θ=45°
θ=105°

12. Properties of Vectors
Vectors can be moved parallel to themselves in a diagram, as long as the magnitude stays the same.
The horizontal vector is moved and doesn’t change the problem as long as the magnitude doesn’t change and it remains parallel to its original position.

13. Properties of Vectors
2. Vectors can be added in any direction. Ex: A+B+C+D+E= Resultant B+A+D+C+E= Resultant E E
Resultant
Resultant C D D C A B B A

14. Properties of Vectors 3. To subtract a vector, add its opposite
A - B = A + (-B)

15. Properties of Vectors
4. Multiplying or dividing vectors by scalars results in vectors.
3 • A = 3A