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AIEEE 2012 Solved Paper
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© examsnet.com
Question : 83
Total: 89
If the line
x
−
1
2
=
y
+
1
3
=
z
−
1
4
and
x
−
3
1
=
y
−
k
2
=
z
1
intersect, then
k
is equal to:
−
1
2
9
9
2
0
Validate
Solution:
Given lines in vector form are
→
r
=
(
∧
i
−
→
j
+
→
k
)
+
λ
(
2
→
i
+
3
→
j
+
→
4
j
)
and
→
r
=
(
3
∧
i
+
k
∧
j
)
+
µ
(
∧
i
+
2
∧
j
+
∧
k
)
These will intersect if shortest distance between them
=
0
i.e.
(
→
a
2
−
→
a
1
)
⋅
→
b
1
×
→
b
2
=
0
⇒
|
3
−
1
k
+
1
−
1
2
3
4
1
2
1
|
=
0
⇒
2
(
−
5
)
−
(
k
+
1
)
(
−
2
)
−
1
(
1
)
=
0
⇒
k
=
9
∕
2
© examsnet.com
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