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Byju's Answer
Standard XII
Mathematics
Pair of Lines
Find the equa...
Question
Find the equation of the plane passing through the intersection of the planes 2x + 3y − z + 1 = 0 and x + y − 2z + 3 = 0 and perpendicular to the plane 3x − y − 2z − 4 = 0.
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Solution
The equation of the plane passing through the line of intersection of the given planes is
2
x
+
3
y
-
z
+
1
+
λ
x
+
y
-
2
z
+
3
=
0
2
+
λ
x
+
3
+
λ
y
+
-
1
-
2
λ
z
+
1
+
3
λ
=
0
.
.
.
1
This plane is perpendicular to 3
x
-
y
-
2
z
-
4
=
0
.
So,
3
2
+
λ
-
3
+
λ
-
2
-
1
-
2
λ
=
0
(Because
a
1
a
2
+
b
1
b
2
+
c
1
c
2
=
0
)
⇒
6
+
3
λ
-
3
-
λ
+
2
+
4
λ
=
0
⇒
6
λ
+
5
=
0
⇒
λ
=
-
5
6
Substituting this in (1), we get
2
-
5
6
x
+
3
-
5
6
y
+
-
1
-
2
-
5
6
z
+
1
+
3
-
5
6
=
0
⇒
7
X
+
13
Y
+
4
z
-
9
=
0
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Similar questions
Q.
Find the equation of plane passing through the intersection of the planes
2
x
+
3
y
−
z
+
1
=
0
and
x
+
y
−
2
z
+
3
=
0
and perpendicular to the plane
3
x
−
y
−
2
z
−
4
=
0
.
Q.
The equation of a plane containing the line of intersection of the planes
2
x
−
y
−
4
=
0
and
y
+
2
z
−
4
=
0
and passing through the point
(
1
,
1
,
0
)
is:
Q.
Find the equation of the plane passing through the intersection of the planes
3
x
−
y
+
2
z
−
4
=
0
and
x
+
y
+
z
+
2
=
0
and the point
(
2
,
2
,
1
)
.
Q.
The plane
x
+
3
y
+
13
=
0
passes through the line of intersection of the planes
2
x
−
8
y
+
4
z
=
p
and
3
x
−
5
y
+
4
z
+
10
=
0
. If the plane is perpendicular to the plane
3
x
−
y
−
2
z
−
4
=
0
, then the value of
p
is
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