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In this chapter we will learn about vectors, (properties, addition, components of vectors)

Chapter 3: Vectors. Reading Assignment: Chapter 4.1-4.3 Homework 3 (due Wednesday, Sept. 7, 2005): Chapter 4: Q9, 4, 7, 11, 12, 22. WebAssign ok? Everything all right in lab? Questions?. In this chapter we will learn about vectors, (properties, addition, components of vectors)

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In this chapter we will learn about vectors, (properties, addition, components of vectors)

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  1. Chapter 3: Vectors Reading Assignment: Chapter 4.1-4.3 Homework 3 (due Wednesday, Sept. 7, 2005): Chapter 4: Q9, 4, 7, 11, 12, 22 • WebAssign ok? • Everything all right in lab? • Questions? • In this chapter we will learn about vectors, (properties, addition, components of vectors) • Multiplication will come later

  2. Multiplying a vector by a scalar The product mA is a vector that has the same _________ as A and magnitude mA. The product –mA is a vector that has the ____________ direction of A and magnitude mA. Examples: 5A; -1/3A

  3. Components of a vector The x- and y-components of a vector: The of a vector: The angle q between vector and x-axis:

  4. The signs of the components Ax and Ay depend on the _____________ and they can be positive or negative. (Examples)

  5. Unit vectors • A unit vector is a __________ vector having a magnitude 1. • Unit vectors are used to indicate a _______________. • i, j, k represent unit vectors along the x-, y- and z- direction • i, j, k form a _______________________ coordinate system

  6. The ____________________ for the vector A is: A = Axi + Ayj

  7. Vector addition using unit vectors: We want to calculate: R = A + B From diagram: R = (Axi + Ayj) + (Bxi + Byj) R = (Ax + Bx)i + (Ay + By)j Rx = Ax+ Bx Ry = Ay+ By The components of R:

  8. Vector addition using unit vectors: The magnitude of a R: The angle q between vector R and x-axis:

  9. Blackboard example 3.2 • Once again, dad doesn’t know where he is going. He drives the car • east for a distance of 50 km, • then north for 30 km • and then in a direction 30° east of north for 25 km. • Sketch the vector diagram for this trip. • Determine the components of the car’s resultant displacement R for the trip. Find an expression for R in terms of unit vectors. • Determine magnitude and direction (angle) of the car’s total displacement R.

  10. Polar Coordinates A point in a plane: Instead of x and y coordinates a point in a plane can be represented by its polar coordinates r and q.

  11. Blackboard example 3.3 The Cartesian coordinates of a point in the x-y plane are (x,y) = (-3.50, -2.50). Find the polar coordinates of this point.

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