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JEE Main 8 Apr 2024 Shift 2 Solved Paper
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© examsnet.com
Question : 13
Total: 90
Let
→
a
=
4
^
i
−
^
j
+
^
k
,
→
b
=
11
^
i
−
^
j
+
^
k
and
→
c
be a vector such that
(
→
a
+
→
b
)
×
→
c
=
→
c
×
(
−
2
→
a
+
3
→
b
)
.
If
(
2
→
a
+
3
→
b
)
⋅
→
c
=
1670
, then
|
→
c
|
2
is equal to :
[8 Apr 2024 Shift 2]
1627
1618
1600
1609
Validate
Solution:
👈: Video Solution
(
→
a
+
→
b
)
×
→
c
−
→
c
×
(
−
2
→
a
+
3
→
b
)
=
0
(
→
a
+
→
b
)
×
→
c
+
(
−
2
→
a
+
3
→
b
)
×
→
c
=
0
⇒
(
→
a
+
→
b
)
−
2
→
a
+
3
→
b
)
×
→
c
=
0
⇒
→
c
=
λ
(
4
→
b
−
→
a
)
⇒
=
λ
(
44
^
i
−
4
^
j
+
4
^
k
−
4
^
i
+
^
j
−
^
k
)
=
λ
(
40
^
i
−
3
^
j
+
3
^
k
)
Now
(
8
^
i
−
2
^
j
+
2
^
k
+
33
^
i
−
3
^
j
+
3
^
k
)
⋅
λ
(
40
^
i
−
3
^
j
+
3
^
k
)
=
1670
⇒
(
41
^
i
−
5
^
j
+
5
^
k
)
⋅
(
40
^
i
−
3
^
j
+
3
^
k
)
×
λ
=
1670
)
⇒
(
1640
+
15
+
15
)
λ
=
1670
⇒
λ
=
1
so
→
c
=
40
^
i
−
3
^
j
−
3
^
k
⇒
|
→
c
|
2
=
1600
+
9
+
9
=
1618
© examsnet.com
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