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JEE Main 26 June 2022 Shift 2 Solved Paper
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© examsnet.com
Question : 16
Total: 90
Let
→
a
=
^
i
+
^
j
+
2
^
k
,
→
b
=
2
^
i
−
3
^
j
+
^
k
and
→
c
=
^
i
−
^
j
+
^
k
be three given vectors. Let
→
v
be a vector in the plane of
→
a
and
→
b
whose projection on
→
c
is
2
√
3
. If
→
v
⋅
^
j
=
7
, then
→
v
⋅
(
^
i
+
^
k
)
is equal to :
[26-Jun-2022-Shift-2]
6
7
8
9
Validate
Solution:
👈: Video Solution
Let
→
v
=
λ
1
→
a
+
λ
2
→
b
, where
λ
1
,
λ
2
∈
R
=
(
λ
1
+
2
λ
2
)
^
i
+
(
λ
1
−
3
λ
2
)
^
j
+
(
2
λ
1
+
λ
2
)
^
k
∵
Projection of
→
v
on
→
c
is
2
√
3
∴
λ
1
+
2
λ
2
−
λ
1
+
3
λ
2
+
2
λ
1
+
λ
2
√
3
=
2
√
3
∴
λ
1
+
3
λ
2
=
1
.
.
.
(i)
and
→
v
⋅
^
j
=
7
⇒
λ
1
−
3
λ
2
=
7
.
.
.
(ii)
from equation (i) and (ii)
λ
1
=
4
,
λ
2
=
−
1
∴
→
v
=
2
^
i
+
7
^
j
+
7
^
k
∴
→
v
⋅
(
^
i
+
^
k
)
=
2
+
7
=
9
© examsnet.com
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