9 7 vectors
This presentation is the property of its rightful owner.
Sponsored Links
1 / 13

9.7 Vectors PowerPoint PPT Presentation


  • 83 Views
  • Uploaded on
  • Presentation posted in: General

9.7 Vectors. Geometry Mrs. Spitz Spring 2005. 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. Also complete Ch. 9 Review: pp. 582-584 #1-24 all.

Download Presentation

9.7 Vectors

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


9 7 vectors

9.7 Vectors

Geometry

Mrs. Spitz

Spring 2005


Objectives

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. Also complete Ch. 9 Review: pp. 582-584 #1-24 all.

  • Reminder: Ch. 9 Test is next week Wednesday. IF you are leaving early, please take the exam early during study hall


Pay attention

Pay attention:

  • I’m 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.


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).

Finding the magnitude of a vector

Q(-6, 3)

P(0, 0)


Write the component form

Here you write the following

Component Form =‹x2 – x1, y2 – y1›

<-6 – 0, 3 – 0>

<-6, 3> is the component form.

Next use the distance formula to find the magnitude.

|PQ| = √(-6 – 0)2 + (3 – 0)2

= √62 + 32

= √36 + 9

= √45

≈ 6.7

Write the component form

Q(-6, 3)

P(0, 0)


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.

Graph Initial/Terminal points


Write the component form1

Here you write the following

Component Form =‹x2 – x1, y2 – y1›

<5 – 0, 4 – 2>

<5, 2> is the component form.

Next use the distance formula to find the magnitude.

|PQ| = √(5 – 0)2 + (4 – 2)2

= √52 + 22

= √25 + 4

= √29

≈ 5.4

Write the component form


Graph initial terminal points1

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.

Graph Initial/Terminal points


Write the component form2

Here you write the following

Component Form =‹x2 – x1, y2 – y1›

<-2 – 3, -1 – 4>

<-5, -5> is the component form.

Next use the distance formula to find the magnitude.

|PQ| = √-2 – 3)2 + (-1– 4)2

= √(-5)2 + (-5)2

= √25 + 25

= √50

≈ 7.1

Write the component form


Adding vectors

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.


What does this mean

What does this mean?

  • Adding vectors:

    Sum of two vectors

    The sum of u = <a1,b1> and v = <a2, b2> is

    u + v = <a1 + a2, b1 + b2>

    In other words: add your x’s to get the coordinate of the first, and add your y’s to get the coordinate of the second.


Example

Example:

  • Let u = <3, 5> and v = <-6, 1>

  • To find the sum vector u + v, add the x’s and add the y’s of u and v.

    u + v = <3 + (-6), 5 + (-1)>

    = <-3, 4>

    There are 6 of these on the test Wednesday!!!


Reminders

Reminders:

  • Test Wednesday before you leave

  • Binder Check Wednesday

  • HW: 9.7 is due Friday

  • HW: Chapter 9 Review is due Monday.

  • HW Worksheets 9.5A & B and 9.6A are due also Monday.


  • Login