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Byju's Answer
Standard XII
Mathematics
Distance between Two Parallel Planes
If the lines ...
Question
If the lines
x
1
=
y
2
=
z
3
,
x
−
1
3
=
y
−
2
−
1
=
z
−
3
4
and
x
+
k
3
=
y
−
1
2
=
z
−
2
h
are concurrent then
A
h
=
−
2
,
k
=
−
6
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B
h
=
1
2
,
k
=
2
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C
h
=
6
,
k
=
2
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D
h
=
2
,
k
=
1
2
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Solution
The correct option is
B
h
=
2
,
k
=
1
2
Given,
L
1
:
x
1
=
y
2
=
z
3
-------(i)
L
2
:
x
−
1
3
=
y
−
2
−
1
=
z
−
3
4
-------(ii)
L
3
:
x
+
k
3
=
y
−
1
2
=
z
−
2
λ
-------(iii)
Any point on
L
1
is
(
λ
1
,
2
λ
,
3
λ
1
)
Any point on
L
2
is
(
3
λ
2
+
1
,
−
λ
2
+
2
,
4
λ
2
+
3
)
∴
λ
1
=
3
λ
2
+
1
,
2
λ
1
+
λ
2
=
2
2
λ
1
−
6
λ
2
=
2
2
λ
1
+
λ
2
=
2
–
––––––––––––
–
λ
2
=
0
∴
λ
1
=
1
∴
P
(
1
,
2
,
3
)
L
3
posses through
′
P
′
1
+
k
3
=
2
−
1
2
=
3
−
2
h
∴
1
+
K
=
3
2
,
1
2
=
1
h
∴
k
=
1
2
∴
h
=
2
∴
h
=
2
,
K
=
1
2
Suggest Corrections
0
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Q.
If the lines
x
=
y
2
=
z
,
x
−
2
−
2
=
y
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4
4
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are interesting, then k =
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1
3
=
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−
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4
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and
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are coplanar, then the value of
k
is
Q.
If
∣
∣ ∣ ∣
∣
x
k
x
k
+
2
x
k
+
3
y
k
y
k
+
2
y
k
+
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z
k
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k
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∣
∣ ∣ ∣
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)
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