Vectors

1. Homework Questions

2. Chapter 6
Section 6.1 Vectors

3. Vectors
• These are directed line segments

4. 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

5. Use the distance formula
5
)26()41(
)()(
22
22
=
−+−−−=
−+−=
d
d
yyxxd
• Therefore, RS=QP, so u=v
5
)04()03(
)()(
22
22
=
−+−=
−+−=
d
d
yyxxd

6. Standard Position
• Starts at the origin
• Component Form - <v1, v2>
• Also called the position of the vector of
the point (v1, v2)

7. Plot the vector
• <2, 3>

8. If not in Standard Position…
•V1 = x2-x1
•V2 = y2-y1
OR
•V = < x2-x1,y2-y1>

9. Find the component form:
• P = (-3, 4)
• Q = (4, 9)
• R = (-2, 5)
• S = (2, -8)
• Find PQ
• Find QR
• Find RS

10. Magnitude
2
12
2
12
2
2
2
1
)()( yyxx
OR
vvv
−+−
+=
• This really just means length
• Distance formula

11. Find the magnitude
• Of RS from before

12. v• Find of PS

13. Vector Addition and Scalar
Mult
•u+v = <u1, u2> + <v1, v2>
= < u1+ v1, u2 + v2>
•ku = k<u1, u2>
<ku1, ku2>

14. Solve
•u = <-1, 3>
•v = <4, 7>
•Find u+v
•Find 3u
•Find 2u+(-1)v

15. Direction Angles
v = <|v|cos×, |v|sin×>

16. Finding the components of a vector:
1. Find the components of the vector v with
direction angle 115° and magnitude 6.
|| v
v

17. Examples
2. Find the components of the vector v with
direction angle 120° and magnitude 10.

18. Examples
3. Find the components of the vector v with
direction angle 45° and magnitude 8.

19. Examples
4. Find the components of the vector v with
direction angle 210° and magnitude 24.

20. Finding Direction Angles
5. r = <4, -5>

21. Finding Direction Angles
6. p = 3i + 7j
7. p = -6i + 2j
8. <-3, -8>

22. 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! 