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Byju's Answer
Standard XII
Mathematics
Intersection of a Line and Finding Roots of a Parabola
Find the equa...
Question
Find the equation of the plane that contains the line of intersection of the planes
r
→
·
i
^
+
2
j
^
+
3
k
^
-
4
=
0
,
r
→
·
2
i
^
+
j
^
-
k
^
+
5
=
0
and which is perpendicular to the plane
r
→
·
5
i
^
+
3
j
^
-
6
k
^
+
8
=
0
.
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Solution
The equation of the plane passing through the line of intersection of the given planes is
r
→
.
i
^
+
2
j
^
+
3
k
^
-
4
+
λ
r
→
.
2
i
^
+
j
^
-
k
^
+
5
=
0
r
→
.
1
+
2
λ
i
^
+
2
+
λ
j
^
+
3
-
λ
k
^
-
4
+
5
λ
=
0
.
.
.
1
This plane is perpendicular to
r
→
.
5
i
^
+
3
j
^
-
6
k
^
+
8
=
0
.
So,
5
1
+
2
λ
+
3
2
+
λ
-
6
3
-
λ
=
0
(Because
a
1
a
2
+
b
1
b
2
+
c
1
c
2
=
0
)
⇒
5
+
10
λ
+
6
+
3
λ
-
18
+
6
λ
=
0
⇒
19
λ
-
7
=
0
⇒
λ
=
7
19
Substituting this in (1), we get
r
→
.
1
+
2
7
19
i
^
+
2
+
7
19
j
^
+
3
-
7
19
k
^
-
4
+
5
7
19
=
0
⇒
r
→
.
33
i
^
+
45
j
^
+
50
k
^
=
41
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0
Similar questions
Q.
Find the equation of the plane which contains the line of intersection of the planes
→
r
.
(
ˆ
i
+
2
ˆ
j
+
3
ˆ
k
)
−
4
=
0
,
→
r
.
(
2
ˆ
i
+
ˆ
j
−
ˆ
k
)
+
5
=
0
and which is perpendicular to the plane
→
r
.
(
5
ˆ
i
+
3
ˆ
j
−
6
ˆ
k
)
+
8
=
0.
Q.
Find the equation of the plane through the point
2
i
^
+
j
^
-
k
^
and passing through the line of intersection of the planes
r
→
·
i
^
+
3
j
^
-
k
^
=
0
and
r
→
·
j
^
+
2
k
^
=
0
.
Q.
Find the equation of the plane which contains the line of intersection of the planes
→
r
.
(
ˆ
i
−
2
ˆ
j
+
3
ˆ
k
)
−
4
=
0
and
→
r
.
(
−
2
ˆ
i
+
ˆ
j
+
ˆ
k
)
+
5
=
0
and whose intercept on X-axis is equal to that of on Y-axis.
Q.
The cartesian equation of the plane passing through the line of intersection of the planes
r
.
(
2
¯
i
+
3
¯
j
+
4
¯
¯
¯
k
)
=
1
and
r
.
(
¯
i
−
¯
j
)
+
4
=
0
and perpendicular to the plane
r
.
(
2
¯
i
−
¯
j
+
¯
¯
¯
k
)
=
0
is
Q.
The vector equation of the line of intersection of the planes
r
.
(
i
+
2
j
+
3
k
)
=
0
and
r
.
(
3
i
+
2
j
+
k
)
=
0
is
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