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JEE Main Math Class 12 Vector Algebra Part 3 Questions
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© examsnet.com
Question : 31
Total: 70
Let
→
a
and
→
b
be two vectors such that
|
→
a
|
=
1
,
|
→
b
|
=
4
and
→
a
⋅
→
b
=
2
. If
→
c
=
(
2
→
a
×
→
b
)
−
3
→
b
and the angle between
→
b
and
→
c
is
α
, then
192
s
i
n
2
α
is equal to____
[31-Jan-2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
→
b
⋅
→
c
=
(
2
→
a
×
→
b
)
⋅
→
b
−
3
|
b
|
2
|
b
|
|
c
|
cos
α
=
−
3
|
b
|
2
|
c
|
cos
α
=
−
12
,
as
|
b
|
=
4
→
a
⋅
→
b
=
2
cos
θ
=
1
2
⇒
θ
=
π
3
|
c
|
2
=
|
(
2
→
a
×
→
b
)
−
3
→
b
|
2
=
64
×
3
4
+
144
=
192
|
c
|
2
cos
2
α
=
144
192
cos
2
α
=
144
192
s
i
n
2
α
=
48
© examsnet.com
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