This worksheet should help with your geometric visualization and under
standing, which will help you with other problems in this chapter. Also,
there may be quiz or test problems which are similar some of these ques
tions.
1. Suppose that
a
and
b
are nonzero vectors.
(a) Show by examples that comp
a
b
and comp
b
a
can be the same and
can be diFerent. What conditions on
a
and
b
will guarantee they
are the same?
(b) Your friend who skips class frequently says, “I’m confused. Isn’t
a
·
b
=
b
·
a
? If that is true, how can comp
a
b
and comp
b
a
be
diFerent?” What is your answer?
(c) Show by examples that proj
a
b
and proj
b
a
can be the same and
can be diFerent. What conditions on
a
and
b
will guarantee they
are the same?
2. Decide for each expression below whether it is a vector (
V
), a scalar
(
S
), or nonsense (
N
). Note that
a
,
b
,
u
, and
v
are vectors, while
c
and
d
are scalars.
Circle one:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Smith
 Math, Euclidean geometry, coordinate planes

Click to edit the document details