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UPSC NDA Math Model Paper 8
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© examsnet.com
Question : 84
Total: 120
If the lines
x
1
=
y
−
2
λ
=
z
+
3
3
and
x
−
2
2
=
y
−
6
3
=
z
−
3
4
are coplanar then find the value of
λ
?
1
2
3
None of these
Validate
Solution:
Given: The lines
x
1
=
y
−
2
λ
=
z
+
3
3
and
x
−
2
2
=
y
−
6
3
=
z
−
3
4
are coplanar
Here, we have to find the value of λ
As we know that, if two lines
x
−
x
1
a
1
=
y
−
y
1
b
1
=
z
−
z
1
c
1
and
x
−
x
2
a
2
=
y
−
y
2
b
2
=
z
−
z
2
c
2
are coplanar then
|
x
2
−
x
1
y
2
−
y
1
z
2
−
z
1
a
1
b
1
c
1
a
2
b
2
c
2
|
=
0
Here,
x
1
=
0
,
y
1
=
2
,
z
1
=
−
3
,
a
1
=
1
,
b
1
=
λ
,
c
1
=
3
Similarly,
x
2
=
2
,
y
2
=
6
,
z
2
=
3
,
a
2
=
2
,
b
2
=
3
and
c
2
=
4
⇒
|
2
4
6
1
λ
3
2
3
4
|
=
0
⇒
2
×
(
4
λ
−
9
)
−
4
×
(
4
−
6
)
+
6
×
(
3
−
2
λ
)
=
0
⇒
8
λ
−
18
+
8
+
18
−
12
λ
=
0
⇒
λ
=
2
Hence. option
B
is the correct answer.
© examsnet.com
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