Gauthier, Joseph – Homework 5 – Due: Sep 29 2007, 3:00 am – Inst: JEGilbert
2
therefore, we see that
c
=
‡
(

1)(

3)

(2)(

2)
·
i
+
‡
(

1)(1)

(2)(2)
·
j
+
‡
(

1)(3)

(2)(3)
·
k
.
Consequently,
c
= 7
i

5
j

9
k
.
keywords: vectors, vector sum, linear combi
nation
004
(part 1 of 1) 10 points
Determine the length of the vector

2
a

b
when
a
=
h 
1
,

2
,
2
i
,
b
=
h
3
,
2
,

1
i
.
1.
length = 2
√
2
2.
length =
√
10
3.
length = 2
√
3
4.
length =
√
14
correct
5.
length =
√
6
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 
1
,

2
,
2
i
,
b
=
h
3
,
2
,

1
i
,
and
c
=

2
a

b
=
h 
1
,
2
,

3
i
,
we see that
 
2
a

b

=
√
14
.
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

2
j

3
k
.
1. n
=
3
5
i

1
5
j

3
10
k
2. n
=
2
3
i
+
2
9
j
+
1
3
k
3. n
=
6
7
i
+
2
7
j
+
3
7
k
4. n
=
6
7
i

2
7
j

3
7
k correct
5. n
=
2
3
i

2
9
j

1
3
k
6. n
=
3
5
i
+
1
5
j
+
3
10
k
Explanation:
The vector
v
= 6
i

2
j

3
k
.
has length

v

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

v

=
6
7
i

2
7
j

3
7
k
is a unit vector having the same direction as
v
.
keywords: vector, length, unit vector,