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Byju's Answer
Standard VIII
Mathematics
The Orthocentre
Find the equa...
Question
Find the equation of the plane passing through the point
(
1
,
−
1
,
2
)
and perpendicular to the planes
2
x
+
3
y
−
3
z
=
2
and
5
x
−
4
y
+
z
=
6
.
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Solution
Let the equation of the plane containing the given point
(
1
,
−
1
,
2
)
is
A
(
x
−
x
1
)
+
B
(
y
−
y
1
)
+
C
(
z
−
z
1
)
=
0
(
i
.
e
)
A
(
x
−
1
)
+
B
(
y
+
1
)
+
C
(
z
−
2
)
=
0
Applying the condition of perpendicular to the plane in equation (1) with the plane
2
x
+
3
y
−
2
z
=
5
and
x
+
2
y
−
3
z
=
8
We have,
2
A
+
3
B
−
2
C
=
0
and
A
+
2
B
−
3
C
=
0
Let us solve three two equations, we get
A
=
−
5
C
B
=
4
C
The required equation is
−
5
C
(
x
−
1
)
+
4
C
(
y
+
1
)
+
c
(
z
−
2
)
=
0
5
x
−
4
y
−
z
−
7
=
0
5
x
−
4
y
−
z
=
7
Hence, this is the answer.
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