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9.4 Vectors

9.4 Vectors. Chapter 9 Right Triangle Trig. Vector : any quantity with magnitude (size) and direction Use an arrow for vector: KW. Magnitude : corresponds to the distance from initial point K to the terminal point W.

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9.4 Vectors

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  1. 9.4 Vectors Chapter 9 Right Triangle Trig

  2. Vector: any quantity with magnitude (size) and direction Use an arrow for vector: KW Magnitude: corresponds to the distance from initial point K to the terminal point W You can also use an ordered pair (x, y) in the coordinate plane for a vector. The magnitude and direction correspond to the distance and direction from the origin.

  3. Example 1, pg 490 Describe OL as an ordered pair. Give the coordinates to the nearest tenth. x O 50 y 65 L

  4. Example 1b, pg 491 Describe the vector as an ordered pair. Give the coordinates to the nearest tenth. 51 y 65 x

  5. Example 2, pg 491Describing a Vector Direction Use Compass directions to describe the direction of each vector. a. b. N N 35 W E W E 25 S S

  6. Example 2, pg 491Describing a Vector Direction Sketch a vector that has the direction 30 west of north. Give a second description for the direction of this vector. N 30 E W S

  7. Example 3, pg 491Aviation An airplane lands 40 km west and 25 km south from where it took off. The result of the trip can be described by the vector (-40, -25). Use distance and direction to described this vector a second way. N -40 W E x -25 c S

  8. Example 3b, pg 491 A small airplane lands at a point 246 mi east and 76 mi north of the point from which it took off. Describe the magnitude and the direction of its flight vector.

  9. Example 3b, pg 491 A small airplane lands at a point 246 mi east and 76 mi north of the point from which it took off. Describe the magnitude and the direction of its flight vector. N 76 mi x W E 246 mi y S

  10. Adding Vectors You can also use a single lowercase letter, such as u, to name a vector. This map shows vectors representing a flight from Houston to Memphis with a stopover in New Orleans. Memphis The vector from Houston to Memphis is called the sum or resultant of the other two vectors. w = u + v w v New Orleans Houston u

  11. Adding Vectors You can add vectors by adding their coordinates. You can also show the sum geometrically. Example 4, pg 492 Vectors a (4, 3) and c (-1, 2) are shown in the diagram. Write the sum of the two vectors as an ordered pair. Then draw e, the sum of a and c. (4, 3) + (-1, 2) = 4 + (-1), 3 + 2 = (3, 5)

  12. Adding Vectors Write the sum of the two vectors (2, 3) and (-4, -2) as an ordered pair. 2 + (-4), 3 + (-2) (-2, 1)

  13. Real-World ConnectionNavigation, Example 5, pg 493 A ferry shuttles people from one side of a river to the other. The speed of the ferry in still water is 25 mi/h. The river flows directly south at 7 mi/h. If the ferry heads directly west, what are the ferry’s resultant speed and direction? N w E S

  14. Questions? Homework: pg 493 1-28

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