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UPSC NDA Math Model Paper 2
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© examsnet.com
Question : 90
Total: 120
If the lines
x
−
1
2
=
y
−
2
3
=
z
−
3
4
and
x
−
2
3
=
y
−
3
4
=
z
−
4
λ
are coplanar then find the value of λ ?
3
4
2
5
Validate
Solution:
Given: The lines
x
−
1
2
=
y
−
2
3
=
z
−
3
4
and
x
−
2
3
=
y
−
3
4
=
z
−
4
λ
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
=
1
,
y
1
=
2
,
z
1
=
3
,
a
1
=
2
,
b
1
=
3
,
c
1
=
4
Similarly,
x
2
=
2
,
y
2
=
3
,
z
2
=
4
,
a
2
=
3
,
b
2
=
4
and
c
2
=
λ
⇒
|
1
1
1
2
3
4
3
4
λ
|
=
0
⇒
1
×
(
3
λ
−
16
)
−
1
×
(
2
λ
−
12
)
+
1
×
(
8
−
9
)
=
0
⇒
3
λ
−
16
−
2
λ
+
12
−
1
=
0
⇒
λ
=
5
Hence. option D is the correct answer.
© examsnet.com
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