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Byju's Answer
Standard XII
Mathematics
Point Form of Normal: Ellipse
Find the equa...
Question
Find the equation of the plane that contains the point (1, −1, 2) and is perpendicular to each of the planes 2x + 3y − 2z = 5 and x + 2y − 3z = 8.
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Solution
The equation of any plane passing through (1, -1, 2) is
a
x
-
1
+
b
y
+
1
+
c
z
-
2
=
0
.
.
.
1
It is given that (1) is perpendicular to the plane 2
x
+
3
y
-
2
z
=
5
.
So
,
2
a
+
3
b
-
2
c
=
0
.
.
.
2
It is given that (1) is perpendicular to the plane
x
+
2
y
-
3
z
=
8
.
So,
a
+
2
b
-
3
c
=
0
.
.
.
3
Solving (1), (2) and (3), we get
x
-
1
y
+
1
z
-
2
2
3
-
2
1
2
-
3
=
0
⇒
-
5
x
-
1
+
4
y
+
1
+
1
z
-
2
=
0
⇒
5
x
-
4
y
-
z
=
7
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