Chapter 6: Vectors

Math 566, Jan 9, 2013
Chapter 6: Vectors
When we add vectors, we place them tip to tail.
1
To do this, we simply move them.
3 m
5 m
u
v
u+v=
2
To subtract, we add the opposite.
3 m
5 m
u
v
u ­v=
3
To subtract, we add the opposite.
3 m
5 m
u
v
u ­v=
4
The vectors involved are not always
parallel.
5 m
u
v
5 m
u+v=
5
It's easy on a grid.
v
u
u+v=
6
7
It's easy on a grid.
v
u
u ­v=
8
It's easy on a grid.
v
u
u ­v=
9
Chasles Relation makes adding several
vectors easy.
D
B
A
C
AB + BC + CD = 10
Chasles Relation makes adding several
vectors easy.
D
B
A
C
BD + DC ­ BC = 11
Chasles Relation makes adding several
vectors easy.
D
B
A
C
BD + DC ­ BC = 12
Components make it easy too.
v = (3, 2)
u = (­2, 1)
u+v=
13
Components make it easy too.
v = (3, 2)
u = (­2, 1)
u+v=
14
Components make it easy too.
v = (3, 2)
u = (­2, 1)
2u ­ 3v =
15
Components make it easy too.
v = (3, 2)
u = (­2, 1)
2u ­ 3v =
16
Components make it easy too.
v = (3, 2)
u = (­2, 1)
2u ­ 3v =
17
Chasles Relation in a parallelogram
Consider parallelogram ABCD. Simplify:
B
A
C
D
18
Chasles Relation in a parallelogram
Consider parallelogram ABCD. Simplify:
B
A
C
D
19
Assignment: Vector Addition Exercise
pages 280 ­ 281: questions 7, 10, 11
20