1. Introduction to Vectors
Lesson 10.3

2. Scalars vs. Vectors Scalars Vectors
Quantities that have size but no direction
Examples: volume, mass, distance, temp
Vectors
Quantities that have both size and direction
Examples
Force
Velocity
Magnetic fields
Size
Terminal point
Initial point

3. Vectors Representation Magnitude of a vector Equivalent vectorsB
Representation
Boldface letters n or S
Letters with arrows over them
Magnitude of a vector
Length of the vector, always positive
Designated |K|
Equivalent vectors
Same magnitude and
Same direction C

4. Resultant Vectors Given vectors
The resultant vector (of both vectors added together) is vector
We say
Note that this is the diagonal of a parallelogram
Can be determined by trigonometric methods D B

5. Vector Subtraction The negative of a vector is a vector with … So
The same magnitude
The opposite direction So
- V V P Q S T

6. Try It Out Given vectors shown Sketch specified resultant vectors A FB

7. Also called "resolving" a vector
Component Vectors
Any vector can be represented as the sum of two other vectors
Usually we represent a vector as components of a horizontal and a vertical vector
Also called "resolving" a vector

8. Position Vector Given a point P in the coordinate plane
Then is the position vector for point P
Component vectors determined by
Px = |P| cos θ
Py = |P| sin θ
• P (x,y) θ O

9. Finding Components Given a vector with magnitude 16 and θ = 212°
What are the components?
θ = 212° 16

10. Application
A cable supporting a tower exerts a force of 723N at an angle of 52.7°
Resolve this force into its vertical and horizontal components
Vx = _______
Vy = _______
723N
52.7°

11. Magnitude and Direction
Given horizontal and vertical components
Vx and Vy
Magnitude found using distance formula
Direction, θRef, found with arctan

12. How Magnitudinous It Is
Given vector B with Bx = 10 and By = -24
Determine magnitude and reference angle.
θ = ?
|B| = ?

13. Assignment
Lesson 10.3
Page 420
Exercises 1 – 35 odd