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Vectors …an introduction

Vectors …an introduction. Objectives of this Section Graph Vectors Add and Subtract Vectors. Vectors in the plane can be represented by arrows , as they are a directed segment. A vector is a quantity that has both magnitude and direction . .

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Vectors …an introduction

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

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

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

  7. N 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 ! Direction“BEARING” of 026° Magnitude 620 MILES

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

  9. San Diego to Boise an example of “Vector Addition” 1st flight SAN to SLC 2nd 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. Vector Addition Tip to Tail & You’ll Never Fail

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

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

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

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

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

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