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JEE Main Math Class 12 Three Dimensional Geometry Part 3 Questions
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© examsnet.com
Question : 53
Total: 134
Let
λ
1
,
λ
2
be the values of
λ
for which the points
(
5
2
,
1
,
λ
)
and
(
−
2
,
0
,
1
)
are at equal distance from the plane
2
x
+
3
y
−
6
z
+
7
=
0
. If
λ
1
>
λ
2
, then the distance of the point
(
λ
1
−
λ
2
,
λ
2
,
λ
1
)
from the line
x
−
5
1
=
y
−
1
2
=
z
+
7
2
is ________.
[8-Apr-2023 shift 1]
Your Answer:
Validate
Solution:
2
x
+
3
y
−
6
z
+
7
=
0
(
5
2
,
1
,
λ
)
,
(
−
2
,
0
,
1
)
d
1
=
|
5
+
3
−
6
λ
+
7
7
|
=
d
2
=
|
−
4
−
6
+
7
7
|
⇒
|
15
−
6
λ
|
=
|
3
|
15
−
6
λ
=
3
or
15
−
6
λ
=
−
3
6
λ
=
12
6
λ
=
18
λ
=
2
λ
=
3
λ
1
=
3
,
λ
2
=
2
∴
P
(
1
,
2
,
3
)
x
−
5
1
=
y
−
1
2
=
z
+
7
2
d
=
|
(
4
,
−
1
,
−
10
)
×
(
1
,
2
,
2
)
3
|
=
|
18
^
i
−
18
^
j
+
9
^
k
3
|
=
9
© examsnet.com
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