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JEE Main 22 July 2021 Shift 2 Solved Paper
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Section:
Mathematics
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© examsnet.com
Question : 66
Total: 90
Let a vector
→
a
be coplanar with vectors
→
b
=
2
^
i
+
^
j
+
^
k
and
→
c
=
^
i
−
^
j
+
^
k
. If
→
a
is perpendicular to
→
d
=
3
^
i
+
2
^
j
+
6
^
k
, and
|
→
a
|
=
√
10
. Then a possible value of
[
→
a
→
b
→
c
]
+
[
→
a
→
b
→
d
]
+
[
→
a
→
c
→
d
]
equal to:
[22 Jul 2021 Shift 2]
−
42
−
40
−
29
−
38
Validate
Solution:
→
a
=
λ
→
b
+
µ
→
c
=
^
i
(
2
λ
+
µ
)
+
^
j
(
λ
−
µ
)
+
^
k
(
λ
+
µ
)
→
a
.
→
d
=
0
=
3
(
2
λ
+
µ
)
+
2
(
λ
−
µ
)
+
6
(
λ
+
µ
)
⇒
14
λ
+
7
µ
=
0
⇒
µ
=
−
2
λ
⇒
→
a
=
(
0
)
^
i
−
3
λ
^
j
+
(
−
λ
)
^
k
⇒
|
→
a
|
=
√
10
|
λ
|
=
√
10
⇒
|
λ
|
=
1
⇒
λ
=
1
or
−
1
[
→
a
→
b
→
c
]
=
0
[
→
a
→
b
→
c
]
+
[
→
a
→
b
→
d
]
+
[
→
a
→
c
→
d
]
=
[
→
a
→
b
+
→
c
→
d
]
=
|
0
−
3
λ
λ
3
0
2
3
2
6
|
=
3
λ
(
12
)
+
λ
(
6
)
=
42
λ
=
−
42
© examsnet.com
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