) We have
1ar  =
ˆ
ˆ
2ˆ
4
i
j
k
+
−
, 
2ar
 = 
ˆ
ˆ
ˆ
3
3
5
i
j
k
+
−
 and b
r
 = 
ˆ
ˆ
ˆ
2
3
6
i
j
k
+
+
Therefore, the distance between the lines is given by
d =
2
1
(
)
| |
b
a
a
b
×
−
r
r
r
r
 = 
ˆ
ˆ
ˆ
2
3
6
2
1
1
4
9
36
i
j
k
−
+
+
or
=
ˆ
ˆ
ˆ
|
9
14
4
|
293
7293
49
49
i
j
k
−
+
−
=
=
EXERCISE 11 2
1 Show that the three lines with direction cosines
12
3
4
4
12
3
3
4
12
,
,
;
,
,
;
,
,
13
13
13
13
13
13
13
13
13
−
−
−
 are mutually perpendicular 2