Miller, Kierste – Homework 5 – Due: Sep 29 2007, 3:00 am – Inst: JEGilbert
2
therefore, we see that
c
=
‡
(1)(

2) + (2)(2)
·
i
+
‡
(1)(3) + (2)(1)
·
j
+
‡
(1)(2) + (2)(2)
·
k
.
Consequently,
c
= 2
i
+ 5
j
+ 6
k
.
keywords: vectors, vector sum, linear combi
nation
004
(part 1 of 1) 10 points
Determine the length of the vector
a

2
b
when
a
=
h
3
,
2
,

1
i
,
b
=
h 
2
,
2
,

1
i
.
1.
length = 3
√
6
correct
2.
length = 2
√
13
3.
length =
√
58
4.
length = 5
√
2
5.
length = 2
√
14
Explanation:
The length,

c

, of the vector
c
=
h
c
1
, c
2
, c
3
i
is defined by

c

=
q
c
2
1
+
c
2
2
+
c
2
3
.
Consequently, when
a
=
h
3
,
2
,

1
i
,
b
=
h 
2
,
2
,

1
i
,
and
c
=
a

2
b
=
h
7
,

2
,
1
i
,
we see that

a

2
b

= 3
√
6
.
keywords: vectors, vector sum, length, linear
combination
005
(part 1 of 1) 10 points
Find a unit vector
n
with the same direction
as the vector
v
= 6
i
+ 3
j
+ 2
k
.
1. n
=
3
5
i

3
10
j

1
5
k
2. n
=
6
7
i

3
7
j

2
7
k
3. n
=
3
5
i
+
3
10
j
+
1
5
k
4. n
=
6
7
i
+
3
7
j
+
2
7
k correct
5. n
=
2
3
i

1
3
j

2
9
k
6. n
=
2
3
i
+
1
3
j
+
2
9
k
Explanation:
The vector
v
= 6
i
+ 3
j
+ 2
k
.
has length

v

=
p
6
2
+ 3
2
+ 2
2
=
√
49 = 7
.
Consequently,
n
=
v

v

=
6
7
i
+
3
7
j
+
2
7
k
is a unit vector having the same direction as
v
.
keywords: vector, length, unit vector,