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Byju's Answer
Standard XII
Mathematics
Equation of Perpendicular from a Point on a Line
The equation ...
Question
The equation of the plane through the point
(
4
,
4
,
0
)
and perpendicular to the plane
x
+
2
y
+
2
z
−
5
=
0
and
3
x
+
3
y
+
2
z
−
8
=
0
is
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Solution
Plane passes through
(
4
,
4
,
0
)
and is perpendicular to
x
+
2
y
+
2
z
−
5
=
0
and
3
x
+
3
y
+
2
z
−
8
=
0
∴
Normal to the plane is
∣
∣ ∣ ∣
∣
^
i
^
j
^
k
1
2
2
3
3
2
∣
∣ ∣ ∣
∣
=
^
i
(
4
−
6
)
−
^
j
(
2
−
6
)
+
^
k
(
3
−
6
)
=
−
2
^
i
+
4
^
j
−
3
^
k
∴
Equation of plane is
−
2
(
x
−
4
)
+
4
(
y
−
4
)
−
3
(
z
−
0
)
=
0
⇒
−
2
x
+
8
+
4
y
−
16
−
3
z
=
0
⇒
−
2
x
+
4
y
−
3
z
−
8
=
0
⇒
2
x
−
4
y
+
3
z
+
8
=
0
Hence, this is the answer.
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