9'7 Vectors

1
9.7 Vectors

• Geometry
• Mrs. Spitz
• Spring 2005

2
Objectives

• This lesson is worth 1/3 of your test grade on
  Thursday.
• Find the magnitude and the direction of the
  vector
• Add vectors
• Assignment pp. 576-577 13-20, 35-40 all. Due
  Thursday
• Also complete Ch. 9 Review pp. 582-584 1-24
  all Due Thursday.
• Reminder Ch. 9 Test Thursday. IF you are
  leaving early, please take the exam tomorrow
  during seminar.

3
Pay attention

• Im only giving you exactly what is on the test.
  There are 4 questions that have to do with
  graphing the vector, putting it into component
  form, and then finding the magnitude. The next
  three examples are good practice and/or notes to
  have on the test Thursday.

4
Finding the magnitude of a vector

• You begin with an initial point to a terminal
  point given in terms of points, usually P and Q.
  You graph it as you would a ray. Initial point
  is P(0, 0). Terminal point is Q(-6, 3).

Q(-6, 3)
P(0, 0)
5
Write the component form

• Here you write the following
• Component Form x2 x1, y2 y1
• lt-6 0, 3 0gt
• lt-6, 3gt is the component form.
• Next use the distance formula to find the
  magnitude.
• PQ v(-6 0)2 (3 0)2
• v62 32
• v36 9
• v45
• 6.7

Q(-6, 3)
P(0, 0)
6
Graph Initial/Terminal points

• Initial point is P(0, 2). Terminal point is Q(5,
  4).
• Reminder that Q is the second point. P is the
  initial point. Graph the ray starting at P and
  going through Q as to the right. Then you can
  start looking for component form and magnitude.

7
Write the component form

• Here you write the following
• Component Form x2 x1, y2 y1
• lt5 0, 4 2gt
• lt5, 2gt is the component form.
• Next use the distance formula to find the
  magnitude.
• PQ v(5 0)2 (4 2)2
• v52 22
• v25 4
• v29
• 5.4

8
Graph Initial/Terminal points

• Initial point is P(3, 4). Terminal point is
  Q(-2, -1).
• Reminder that Q is the second point. P is the
  initial point. Graph the ray starting at P and
  going through Q as to the right. Then you can
  start looking for component form and magnitude.

9
Write the component form

• Here you write the following
• Component Form x2 x1, y2 y1
• lt-2 3, -1 4gt
• lt-5, -5gt is the component form.
• Next use the distance formula to find the
  magnitude.
• PQ v-2 3)2 (-1 4)2
• v(-5)2 (-5)2
• v25 25
• v50
• 7.1

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Adding Vectors

• Two vectors can be added to form a new vector.
  To add u and v geometrically, place the initial
  point of v on the terminal point of u, (or place
  the initial point of u on the terminal point of
  v). The sum is the vector that joins the initial
  point of the first vector and the terminal point
  of the second vector. It is called the
  parallelogram rule because the sum vector is the
  diagonal of a parallelogram. You can also add
  vectors algebraically.

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What does this mean?

• Adding vectors
• Sum of two vectors
• The sum of u lta1,b1gt and v lta2, b2gt is
• u v lta1 a2, b1 b2gt
• In other words add your xs to get the
  coordinate of the first, and add your ys to get
  the coordinate of the second.

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Example

• Let u lt3, 5gt and v lt-6, 1gt
• To find the sum vector u v, add the xs and add
  the ys of u and v.
• u v lt3 (-6), 5 (-1)gt
• lt-3, 4gt
• There are 6 of these on the test Thursday!!!

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Reminders

• Test Thursday before you leave
• Binder Check Thursday
• HW 9.7 is due Thursday
• HW Chapter 9 Review is due Thursday.