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UPSC NDA Math Model Paper 4
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© examsnet.com
Question : 51
Total: 120
If the lines
x
−
2
1
=
y
−
4
4
=
z
−
6
7
and
x
+
1
3
=
y
+
3
5
=
z
+
5
λ
are coplanar then find the value of λ ?
7
5
4
8
Validate
Solution:
Given: The lines
x
−
2
1
=
y
−
4
4
=
z
−
6
7
and
x
+
1
3
=
y
+
3
5
=
z
+
5
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
=
2
,
y
1
=
4
,
z
1
=
6
,
a
1
=
1
,
b
1
=
4
,
c
1
=
7
Similarly,
x
2
=
−
1
,
y
2
=
−
3
,
z
2
=
−
5
,
a
2
=
3
,
b
2
=
5
and
c
2
=
λ
⇒
|
−
3
−
7
−
11
1
4
7
3
5
λ
|
=
0
⇒
−
3
×
(
4
λ
−
35
)
+
7
×
(
λ
−
21
)
−
11
×
(
5
−
12
)
=
0
⇒
−
12
λ
+
105
+
7
λ
−
147
+
77
=
0
⇒
λ
=
7
Hence. option A is the correct answer.
© examsnet.com
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