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Byju's Answer
Standard XII
Mathematics
Distance between Two Parallel Planes
Find the valu...
Question
Find the value of
λ
such that the line
x
−
2
6
=
y
−
1
λ
=
z
+
5
−
4
is perpendicular to the plane
3
x
−
y
−
2
z
=
7
.
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Solution
Let the given line is
x
−
2
6
=
y
−
1
λ
=
z
+
5
−
4
Direction ratios are
6
,
λ
,
−
4
And the given plane
3
x
−
y
−
2
z
=
7
Its direction ratios are
3
,
−
1
,
−
2
And, the given line and plane are perpendicular
then,
6
(
3
)
+
λ
(
−
1
)
+
(
−
4
)
(
−
2
)
=
0
18
−
λ
+
8
=
0
λ
=
26
Hence,
the value of
λ
is
26
.
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Similar questions
Q.
Find the value of λ such that the line
x
-
2
6
=
y
-
1
λ
=
z
+
5
-
4
is perpendicular to the plane 3x − y − 2z = 7.
Q.
Find the value of
λ
such that the line
x
−
2
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=
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Q.
Find the value of
λ
such that the line
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=
y
−
1
λ
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3
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8
is perpendicular to
3
x
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y
−
2
z
=
7
Q.
Find the value of
β
so that the line
x
−
2
6
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=
z
+
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−
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is perpendicular to the plane
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Q.
The value of
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−
5
=
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z
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and
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