day 3 vectors worked

Homework Questions

Chapter 6Section 6.1 Vectors

Vectors

• These are directed line segments

Initial Point vs. Terminal Point

• Let u be the vector from R(-4, 2) to S(-1, 6) and v be the vector from Q(0, 0) to P(3, 4).

• Prove u=v

Use the distance formula

5)26()41(

)()(22

22

dd

yyxxd

• Therefore, RS=QP, so u=v

5)04()03(

)()(22

22

dd

yyxxd

Standard Position

• Starts at the origin• Component Form - <v1, v2>• Also called the position of the vector of

the point (v1, v2)

Plot the vector• <2, 3>

If not in Standard Position…

•V1 = x2-x1

•V2 = y2-y1

OR

•V = < x2-x1, y2-y1>

Find the component form:

• P = (-3, 4)• Q = (4, 9)• R = (-2, 5)• S = (2, -8)

• Find PQ

• Find QR

• Find RS

Magnitude

212

212

22

21

)()( yyxx

OR

vvv

• This really just means length• Distance formula

Find the magnitude • Of RS from before

v• Find of PS

Vector Addition and Scalar Mult•u+v = <u1, u2> + <v1, v2>

= < u1+ v1, u2 + v2>

•ku = k<u1, u2>

<ku1, ku2>

Solve

•u = <-1, 3>• v = <4, 7>• Find u+v

• Find 3u

• Find 2u+(-1)v

Direction Angles

v = <|v|cos×, |v|sin×>

Finding the components of a vector:

1. Find the components of the vector v with direction angle 115° and magnitude 6.

|| vv

Examples


Finding Direction Angles

5. r = <4, -5>

Finding Direction Angles

6. p = 3i + 7j

7. p = -6i + 2j

8. <-3, -8>

HOMEWORK

•Pg. 511 (1-35 odd)•Remember, you can check in the back

of the book to make sure you are doing these correctly! Come with questions ready!

Education