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Byju's Answer
Standard XII
Mathematics
Angle between a Plane and a Line
A plane which...
Question
A plane which passes through the point
(
3
,
2
,
0
)
and the line
x
−
3
1
=
y
−
7
5
=
z
−
4
4
is?
A
x
−
y
+
z
=
1
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B
x
+
y
+
z
=
5
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C
x
+
2
y
−
z
=
1
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D
2
x
−
y
+
z
=
5
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Solution
The correct option is
A
x
−
y
+
z
=
1
Let the equation of plane passing through
(
3
,
2
,
0
)
is
⇒
a
(
x
−
3
)
+
b
(
y
−
2
)
+
c
(
z
−
0
)
=
0
---- ( 1 )
⇒
x
−
3
1
=
y
−
7
5
=
z
−
4
4
pass through
(
3
,
2
,
0
)
and has direction ratios as
1
,
5
,
4
If the equation of plane contains this, it should pass from
(
3
,
7
,
4
)
and parallel to
(
1
,
5
,
4
)
∴
a
(
3
−
1
)
+
b
(
7
−
5
)
+
c
(
4
−
4
)
=
0
⇒
2
a
+
2
b
=
0
⇒
a
+
b
=
0
---- ( 2 )
And
⇒
a
+
5
b
+
4
c
=
0
----- ( 3 )
On solving equation ( 2 ) and ( 3 ) we get,
⇒
a
=
c
and
4
b
=
−
c
Hence, equation of plane will be,
⇒
c
(
x
−
3
)
−
c
(
y
−
2
)
+
c
z
=
0
[ From ( 1 ) ]
⇒
x
−
3
−
y
+
2
+
z
=
0
⇒
x
−
y
+
z
−
1
=
0
⇒
x
−
y
+
z
=
1
Suggest Corrections
0
Similar questions
Q.
The plane which passes through the point
(
3
,
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,
0
)
and the line
x
−
3
1
=
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−
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is:
Q.
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(
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,
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and parallel to the line of the intersection of the plane
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x
1
=
y
2
=
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3
is
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(b) x − 5y + 3z = −7
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(d) x + 5y + 3z = −7
Q.
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(
−
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,
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, parallel to the plane
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+
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and intersecting the line
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y
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is:
Q.
The image of the line
x
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1
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