1. Introduction to Vectors Lesson 10.3

2. 2 Scalars vs. Vectors Scalars  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 Initial point Terminal point Size

3. 3 Vectors Representation  Boldface lettersn 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 B C

4. 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 A B D C

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

6. 6 Try It Out Given vectors shown Sketch specified resultant vectors A B C D E F

7. 7 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. 8 Position Vector Given a point P in the coordinate plane Then is the position vector for point P Component vectors determined by  P x = |P| cos θ  P y = |P| sin θ P (x,y) O θ

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

10. 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  V x = _______  V y = _______ 52.7° 723N

11. 11 Magnitude and Direction Given horizontal and vertical components V x and V y  Magnitude found using distance formula  Direction, θ Ref, found with arctan

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

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