Introduction to Vectors

1. Introduction to Vectors Lesson 10.3

2. Size 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 Terminal point Initial point

3. Vectors B • 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. C Resultant Vectors A • Given vectors • The resultant vector(of both vectors addedtogether) is vector • We say • Note that this is the diagonal of a parallelogram • Can be determined by trigonometric methods D B

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

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

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. θ 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) 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