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Byju's Answer
Standard XII
Mathematics
Pair of Lines
Find the equa...
Question
Find the equation of the plane that is perpendicular to the plane 5x + 3y + 6z + 8 = 0 and which contains the line of intersection of the planes x + 2y + 3z − 4 = 0, 2x + y − z + 5 = 0.
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Solution
The equation of the plane passing through the line of intersection of the given planes is
x
+
2
y
+
3
z
-
4
+
λ
2
x
+
y
-
z
+
5
=
0
1
+
2
λ
x
+
2
+
λ
y
+
3
-
λ
z
-
4
+
5
λ
=
0
.
.
.
1
This plane is perpendicular to 5
x
+
3
y
+
6
z
+
8
=
0
.
So,
5
1
+
2
λ
+
3
2
+
λ
+
6
3
-
λ
=
0
(Because
a
1
a
2
+
b
1
b
2
+
c
1
c
2
=
0
)
⇒
5
+
10
λ
+
6
+
3
λ
+
18
-
6
λ
=
0
⇒
7
λ
+
29
=
0
⇒
λ
=
-
29
7
Substituting this in (1), we get
1
+
2
-
29
7
x
+
2
-
29
7
y
+
3
+
29
7
z
-
4
+
5
-
29
7
=
0
⇒
-
51
x
-
15
y
+
50
z
-
173
=
0
⇒
51
x
+
15
y
-
50
z
+
173
=
0
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0
Similar questions
Q.
Find the equation of the plane which contains the line of intersection of the planes x + 2y + 3z − 4 = 0 and 2x + y − z + 5 = 0 and which is perpendicular to the plane 5x + 3y − 6z + 8 = 0.
Q.
The equation of plane which is perpendicular to the plane
5
x
+
3
y
+
6
z
+
8
=
0
and which contains the line of intersection of the planes
x
+
2
y
+
3
z
−
4
=
0
and
2
x
+
y
−
z
+
5
=
0
is
Q.
The equation of the plane which contains the line of intersection of planes
x
+
2
y
+
3
z
−
4
=
0
and
2
x
+
y
−
z
+
5
=
0
which is perpandicular to the plane
5
x
+
3
y
−
6
z
+
8
=
0
Q.
Find the equation of the plane which is perpendiular to the plane
5
x
+
3
y
+
6
z
+
8
=
0
and which contains the line intersection of the plane
x
+
2
y
+
3
z
−
4
=
0
and
2
x
+
y
−
z
+
5
=
0
Q.
Equation of the plane containing the line
x
+
2
y
+
3
z
−
4
=
0
=
2
x
+
y
−
z
+
5
and perpendicular to the plane
5
x
+
3
y
−
6
z
+
8
=
0
is
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