1. Vectors…an introduction Objectives of this Section Graph Vectors Add and Subtract Vectors

2. A vector is a quantity that has both magnitude and direction. Vectors in the plane can be represented by arrows, as they are a directed segment.

3. The length of the arrow represents the magnitude of the vector. The arrowhead indicates the direction of the vector, which can be measured by a compass or a coordinate system.

4. P Q Initial Point Terminal Point Directed line segment

5. If a vector v has the same magnitude and the same direction as the directed line segment PQ, then we write

6. The vector v whose magnitude is 0 is called the zero vector, 0. if they have the same magnitude and direction. Two vectors v and w are equal, written

7. Vectors & Bearings… it’s like flying a plane Suppose you need to take a plane trip to Salt Lake City from San Diego You’ll need a map and compass to plan the flight ! N Magnitude 620 MILES Direction “BEARING” of 026°

8. Vectors & Bearings… What if you flew from SLC to Denver N Magnitude 379 MILES Direction “BEARING” of 98°

9. San Diego to Boise an example of “Vector Addition” 1 st flight SAN to SLC 2 nd flight SLC to BOISE Then your friend charters a private plane that flies direct to Boise.

10. Let’s look a little closer at Vector Addition

11. Tip to Tail & You’ll Never Fail Vector Addition

12. Use the vectors illustrated below to graph each expression.

14. Vector addition is commutative. V + W= W + V

15. Vector addition is associative. (V + U) +W= V + (U + W) U U

16. Initial point of v Terminal point of w Vector Addition…in summary Just remember… “Tip to Tail” means placing the tip of the 1 st vector and the tail of the second vector at the same point.

17. There’s also Vector Multiplication W + W= 2W 3V