1. Discrete Math Section 12.1 Perform basic operations on vectors Scalars are quantities that are completely described by a magnitude only. Vectors are quantities that are described by a direction and a magnitude. scalars vectors 6 ft 6 ft upward 12 newtons 12 newtons left 75 mph 75 mph east

2. Vectors can be represented by arrows 9 newtons east 4 newtons up 5 newtons at 30 degrees N of E

3. The length of a vector indicates its magnitude. The orientation of the vector indicates its direction. Vectors can named by letters in bold print. The absolute value of a vector is the magnitude. V = 70 ft/s east | V | = 70 ft/s u = 35 newtons down | u | = 35 newtons

4. Vectors can be multiplied by scalars.

5. Vectors can be added or subtracted. http://phet.colorado.edu/en/simulation/vector-addition

6. Trigonometric methods for the resultant of two vectors Law of Cosines a 2 = b 2 + c 2 – 2bc∙cosA Law of Sines sin A = sin B a b

7. Example 1 Make a scale drawing of a force of 50 N west and another force of 30 N on a heading of 210 degrees. Find the resultant graphically and using trigonometry.

8. Example 2 An airplane flies southwest with a velocity of 400 mph. The wind blows toward the east with a velocity of 50 mph. Find the resultant velocity of the plane both graphically and using trigonometry.

9. Assignment Page 423 Problems 1,2,4,8,9,10,12,14a,15 (25ec)