Find the shortest distance between the lines
1
1
1
7
6
1
x
y
z
+
+
+
=
=
−
   and  
3
5
7
1
2
1
x
y
z
−
−
−
=
=
−
16 Find the shortest distance between the lines whose vector equations are
ˆ
ˆ
ˆ
(
2
3 )
r
i
j
k
=
+
+
r
 + 
ˆ
ˆ
ˆ
(
3
2 )
i
j
k
λ
−
+
and  
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
4
5
6
(2
3
)
r
i
j
k
i
j
k
=
+
+
+ µ
+
+
r
17 Find the shortest distance between the lines whose vector equations are
ˆ
ˆ
ˆ
(1
)
(
2)
(3
2 )
r
t i
t
j
t k
=
−
+
−
+
−
r
 and
ˆ
ˆ
ˆ
(
1)
(2
1)
(2
1)
r
s
i
s
j
s
k
=
+
+
−
−
+
r
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THREE D IMENSIONAL G EOMETRY
479
11 6  Plane
A plane is determined uniquely if any one of the following is known:
(i)
the normal to the plane and its distance from the origin is given, i