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JEE Main 4 Apr 2024 Shift 2 Solved Paper
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© examsnet.com
Question : 19
Total: 90
Let
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
2
^
i
+
4
^
j
−
5
^
k
and
→
c
=
x
^
i
+
2
^
j
+
3
^
k
,
x
∈
ℝ
. If
→
d
is the unit vector in the direction of
→
b
+
→
c
such that
→
a
⋅
→
d
=
1
, then
(
→
a
×
→
b
)
⋅
→
c
is equal to
[4 Apr 2024 Shift 2]
9
6
3
11
Validate
Solution:
👈: Video Solution
→
d
=
λ
(
→
b
+
→
c
)
→
a
⋅
→
d
=
λ
(
→
b
⋅
→
a
+
→
c
⋅
→
a
)
1
=
λ
(
1
+
x
+
5
)
1
=
λ
(
x
+
6
)
. . .(1)
|
→
d
|
=
1
1
λ
=
x
+
6
|
λ
(
→
b
+
→
c
)
|
=
1
|
λ
(
(
x
+
2
)
^
i
+
6
^
j
−
2
^
k
)
|
=
1
λ
2
(
(
x
+
2
)
2
+
6
2
+
2
2
)
=
1
x
2
+
4
x
+
4
+
36
+
4
=
(
x
+
6
)
2
x
2
+
4
x
+
44
=
x
2
+
12
x
+
36
8
x
=
8
,
x
=
1
|
1
1
1
2
4
−
5
x
2
3
|
=
(
→
a
×
→
b
)
⋅
→
c
|
0
0
1
−
2
9
−
4
x
−
2
−
1
3
|
=
2
−
9
(
x
−
2
)
=
20
−
9
x
at
x
=
1
20
−
9
=
11
Option 4 is correct
© examsnet.com
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