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VITEEE 2021 Paper
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Section:
Mathematics
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© examsnet.com
Question : 53
Total: 80
The shortest distance between the lines
x
=
y
+
2
=
6
z
−
6
and
x
+
1
=
2
y
=
−
12
z
is
1
2
2
1
3
2
Validate
Solution:
The lines are
x
6
=
y
+
2
6
=
z
−
1
1
and
x
+
1
12
=
y
6
=
z
−
1
Here,
→
a
1
=
−
2
^
j
+
^
k
,
→
b
1
=
6
^
i
+
6
^
j
+
^
k
,
→
a
2
=
−
^
i
→
b
2
=
12
^
i
+
6
^
j
−
^
k
→
b
1
×
→
b
2
=
|
^
i
^
j
k
‌
6
6
1
‌
12
6
−
1
|
=
−
12
^
i
+
18
^
j
−
36
^
k
Shortest distance
=
|
(
→
a
2
−
→
a
1
)
.
(
→
b
1
×
→
b
2
)
|
|
→
b
1
×
→
b
2
|
=
|
(
−
^
i
+
2
^
j
−
^
k
)
(
−
12
i
+
18
^
j
−
36
k
)
|
√
(
−
12
)
2
+
(
18
)
2
+
(
−
36
)
2
=
|
+
12
+
36
+
36
|
√
1764
=
84
42
=
2
© examsnet.com
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