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JEE Mains 12-Apr-2023 Shift 1 Solved Paper
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© examsnet.com
Question : 11
Total: 90
Let
λ
∈
Z
,
→
a
=
λ
^
i
+
^
j
−
^
k
and
→
b
=
3
^
i
−
^
j
+
2
^
k
. Let
→
c
be a vector such that
(
→
a
+
→
b
+
→
c
)
×
→
c
=
→
0
,
→
a
⋅
→
c
=
−
17
and
→
b
⋅
→
c
=
−
20
. Then
|
→
c
×
(
λ
^
i
+
^
j
+
^
k
)
|
2
is equal to
[12-Apr-2023 shift 1]
62
53
49
46
Validate
Solution:
(
→
a
+
→
b
+
→
c
)
×
→
c
=
0
(
→
a
+
→
b
)
×
→
c
=
0
→
c
=
α
(
→
a
+
→
b
)
=
α
(
λ
+
3
)
^
i
+
α
^
k
→
b
⋅
→
c
=
−
20
⇒
3
α
(
λ
+
3
)
+
2
α
=
−
20
→
a
⋅
→
c
=
−
17
⇒
α
λ
(
λ
+
3
)
−
α
=
−
17
⇒
α
(
3
λ
+
9
+
2
)
=
−
20
α
(
λ
2
+
3
λ
−
1
)
=
−
17
17
(
3
λ
+
11
)
=
20
(
λ
2
+
3
λ
−
1
)
20
λ
2
+
9
λ
−
207
=
0
λ
=
3
(
λ
∈
Z
)
⇒
α
=
−
1
⇒
→
c
=
−
(
6
^
i
+
^
k
)
→
v
=
→
c
×
(
3
^
i
+
^
j
+
^
k
)
=
|
^
i
^
j
^
k
−
6
0
−
1
3
1
1
|
=
^
i
+
3
^
j
−
6
^
k
|
→
v
|
2
=
(
−
1
)
2
+
3
2
+
6
2
=
46
© examsnet.com
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