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
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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.