This preview shows pages 1–3. Sign up to view the full content.
[Hand out timesheets and groupwork worksheet]
[Collect truefalse quizzes on 92.141 material]
[Collect summaries of section 10.4]
Section 10.3: The dot product (concluded)
Important fact to keep in mind: For any vector
v
, we have
v
•
v
= …
..?.
.
the length of
v
, squared.
So 
v
 = sqrt(
v
•
v
).
Economics example (Problem 12): A street vendor sells
a
hamburgers,
b
hot dogs, and
c
soft drinks on a given day.
He charges $2 for a hamburger, $1.50 for a hot dog, and $1
for a soft drink.
If
A
=
⟨
a
,
b
,
c
⟩
and
P
=
⟨
2, 1.5, 1
⟩
, what is
the meaning of the dot product
A
•
P
?
..?.
.
The vendor’s revenue.
Physics example: When a forcevector
F
causes an object
to be displaced by the displacement vector
D
, the work
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document done is …
..?.
.
F
•
D
(or
D
•
F
).
(Note that this is negative when the angle is obtuse, or
when
F
and
D
point in opposite directions; e.g., when I
lower a heavy object, I’m doing negative work on it.)
Suppose
a
•
b
=
a
•
c
, with
a
≠
0
.
Can I conclude that
b
=
c
?
..?.
.
No; e.g.,
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.
 Fall '11
 Staff
 Dot Product

Click to edit the document details