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

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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• Everything all right in lab?
• Questions?

• In this chapter we will learn about vectors,
  (properties, addition, components of vectors)
• Multiplication will come later

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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 doesnt 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.

1. Sketch the vector diagram for this trip.
2. Determine the components of the cars resultant
   displacement R for the trip. Find an expression
   for R in terms of unit vectors.
3. Determine magnitude and direction (angle) of the
   cars 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.
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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.