1. Copyright © 2011 Pearson, Inc. 6.1 Vectors in the Plane Day 2

2. Copyright © 2011 Pearson, Inc. Slide 6.1 - 2 What you’ll learn about Two-Dimensional Vectors Vector Operations Unit Vectors Direction Angles Applications of Vectors … and why These topics are important in many real-world applications, such as calculating the effect of the wind on an airplane’s path.

3. Copyright © 2011 Pearson, Inc. Direction Angles A simple but precise way to specify direction of a vector v is to state its direction angle Direction angle – the angle  that v makes with the positive x axis To solve for these components is called Resolving the Vector Slide 6.1 - 3

4. Copyright © 2011 Pearson, Inc. Slide 6.1 - 4 Resolving the Vector

5. Copyright © 2011 Pearson, Inc. Slide 6.1 - 5 Example Finding the Components of a Vector

6. Copyright © 2011 Pearson, Inc. Slide 6.1 - 6 You Try Finding the Components of a Vector Find the components of the vector v with directional angle 115° and magnitude 6.

7. Copyright © 2011 Pearson, Inc. Slide 6.1 - 7 Example Finding the Direction Angle of a Vector

8. Copyright © 2011 Pearson, Inc. Slide 6.1 - 8 Example Finding the Direction Angle of a Vector

9. Copyright © 2011 Pearson, Inc. Slide 6.1 - 9 Example Finding the Direction Angle of a Vector

10. Copyright © 2011 Pearson, Inc. Slide 6.1 - 10 Example Finding the Direction Angle of a Vector o

11. Copyright © 2011 Pearson, Inc. You Try Slide 6.1 - 11

12. Copyright © 2011 Pearson, Inc. Slide 6.1 - 12 Velocity and Speed The velocity of a moving object is a vector because velocity has both magnitude and direction. The magnitude of velocity is speed.

13. Copyright © 2011 Pearson, Inc. Example A DC-10 jet aircraft is flying on a bearing of 65° at 500 mph. Find the component for of the velocity of the airplane. Recall that the bearing is the angle that the line of travel makes with due north, measured clockwise. Slide 6.1 - 13