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JEE Mains 26-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 22
Total: 90
The largest value of
a
, for which the perpendicular distance of the plane containing the lines
→
r
=
(
^
i
+
^
j
)
+
λ
(
^
i
+
a
^
j
−
^
k
)
and
→
r
=
(
^
i
+
^
j
)
+
µ
(
−
^
i
+
^
j
−
a
^
k
)
from the point
(
2
,
1
,
4
)
is
√
3
, is _________.
[26-Jul-2022-Shift-2]
Your Answer:
Validate
Solution:
👈: Video Solution
Normal to plane
=
|
^
i
^
j
^
k
1
a
−
1
−
1
1
−
a
|
=
^
i
(
1
−
a
2
)
−
^
j
(
−
a
−
1
)
+
^
k
(
1
+
a
)
=
(
1
−
a
)
^
i
+
^
j
+
^
k
Distance from
(
2
,
1
,
4
)
is
√
3
i.e.
⇒
|
(
1
−
a
)
+
0
+
4
√
(
1
−
a
)
2
+
1
+
1
|
=
√
3
⇒
25
+
a
2
−
10
a
=
3
a
2
−
6
a
+
9
⇒
2
a
2
+
4
a
−
16
=
0
⇒
a
2
+
2
a
−
8
=
0
a
=
2
or
−
4
∴
a
max
=
2
© examsnet.com
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