4
You visited us
4
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Angle between a Plane and a Line
Find the equa...
Question
Find the equation of the plane through the line of intersection of the planes
x
+
y
+
z
=
1
and
2
x
+
3
y
+
4
z
=
5
which is perpendicular to the plane
x
−
y
+
z
=
3
Open in App
Solution
Equation of plane passing through intersections of the planes
P
1
:
x
+
y
+
z
−
1
=
0
and
P
2
:
2
x
+
3
y
+
4
z
−
5
=
0
is given by,
P
2
+
λ
P
1
=
0
⇒
(
2
+
λ
)
x
+
(
3
+
λ
)
y
+
(
4
+
λ
)
z
−
(
5
+
λ
)
=
0....
(1)
Now for above plane to be perpendicular to the given plane
x
−
y
+
z
=
0
Dot product of their normal vector should be zero
⇒
(
2
+
λ
)
(
1
)
+
(
3
+
λ
)
(
−
1
)
+
(
4
+
λ
)
1
=
0
⇒
3
+
λ
=
0
⇒
λ
=
−
3
Hence the required plane is,
⇒
(
2
−
3
)
x
+
(
3
−
3
)
y
+
(
4
−
3
)
z
−
(
5
−
3
)
=
0
, substitute
λ
=
−
3
in (1)
⇒
−
x
+
z
−
2
=
0
⇒
x
−
z
+
2
=
0
Suggest Corrections
0
Similar questions
Q.
Find the equation of the plane passing through the line of intersection of the planes
x
+
y
+
z
=
1
and
2
x
+
3
y
+
4
z
=
5
which is perpendicular to the plane
x
−
y
+
z
=
0
.
Q.
Find the vector equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x − y + z = 0.
Q.
Find eqn of plane through line of intersection of planes
x
+
y
+
z
=
1
2
x
+
3
y
+
4
z
=
5
which is
⊥
l
a
r
to plane
x
−
y
+
z
=
0
.
Q.
Find the equation of the plane through the line of intersection of the planes
2
x
+
y
−
z
=
3
,
5
x
−
3
y
+
4
z
+
9
=
0
and parallel to line
x
−
1
2
=
y
−
3
4
=
z
−
5
5
.
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Angle between a Plane and a Line
MATHEMATICS
Watch in App
Explore more
RJ Board
Angle between a Plane and a Line
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app