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9.7 Vectors

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9.7 Vectors

Geometry

Mrs. Spitz

Spring 2005

- 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

- 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.

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)

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

Q(-6, 3)

P(0, 0)

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.

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

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.

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

- 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.

- 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.

- 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!!!

- 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.