MATH1850 Midterm 2
November, 2010
2
1. (6 marks)
Find the angle (in degrees) between the two vectors (4, 1, -2) and
(5,-3,1).
Hint:
)
cos(
v
u
v
u
2. (2 marks each; 4 marks total)
Answer each question in the space provided.
a)
Consider the set
W
consisting of all vectors of the form (a, b, 0) where
a
and
b
are
real numbers and
0
a
.
Explain why the following vector space property fails.
“For each
u
in
V
, there is an object
u
in
V
, called the negative of
u
, such that
0
u
u
u
u
)
(
)
(
”.
b)
Consider the set
W
consisting of all vectors of the form (a, b, 1) where
a
and
b
are
real numbers.
Show why the following vector space property fails.
“If
u
and
v
are objects in
V
, then
v
u
is in
V
.

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