1. Physics Quantities
Scalars
and
Vectors

2. Scalar: A quantity that is described by magnitude only.
You add scalar quantities like you normally add numbers.
5 mL of water added to 5 mL of water will give you 10 mL of water.
Some examples of scalars are
Distance
Speed
Mass
Time
Volume.

3. Vector:
A quantity that is described by stating its magnitude and direction.
You must learn special methods to add vectors (see below).
Some examples of vectors are
Displacement
Velocity
Acceleration
Force.

4. Vectors (cont.)
Vectors are represented by arrows (directed line segments).
A vector has a head and a tail.
The length of the arrow, when drawn to some self-determined scale, represents the magnitude of the vector and its direction is the way it points in 3-dimensional space as you sight from tail to head.
Tail Head

5. Vectors (cont.)
They can be added graphically by placing the arrows head to tail.
The arrow that extends from the tail of the first vector to the head of the last vector is called the resultant.
It indicates both the magnitude and direction of the vector sum.
Vector A Vector B
Resultant = Vector A + Vector B

6. Vectors (cont.)
Remember, vectors don't always have to be in a straight line but may be oriented at angles to each other, such as
Vector A Vector B
Resultant = Vector A + Vector B

7. Vectors (cont.) Vectors can be added in any order. Vector B Vector A
Resultant = Vector B + Vector A

8. Vectors (cont.)
Vector A Vector B
Resultant = Vector A + Vector B

9. Vectors (cont.)
More than two vectors can be added together using the head-to-tail method.
Vector A Vector B Vector C Vector D
Resultant = Vector A + Vector B + Vector C + Vector D

10. Vectors (cont.)
Resultant vectors can be determined by a number of different methods. You will solve vector addition exercises both graphically and with vector components.