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AIEEE 2004 Math Solved Paper
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© examsnet.com
Question : 58
Total: 68
Let
→
a
,
→
b
and
→
c
be non-zero vectors such that
(
→
a
×
→
b
)
×
→
c
=
1
3
|
→
b
|
→
c
∣
→
a
. If
θ
is the acute angle between the vectors
→
b
and
→
c
, then
s
i
n
θ
equals
2
√
2
3
√
2
3
2
3
1
3
Validate
Solution:
Given
(
→
a
×
→
b
)
×
→
c
=
1
3
|
→
b
|
|
→
c
|
→
a
Clearly
→
a
and
→
b
are noncollinear
⇒
(
→
a
⋅
→
c
)
→
b
−
(
→
b
⋅
→
c
)
→
a
=
1
3
|
→
b
|
|
→
c
|
→
a
∴
→
a
⋅
→
c
=
0
and
−
→
b
⋅
→
c
=
1
3
|
→
b
|
|
→
c
|
⇒
cos
θ
=
−
1
3
∴
s
i
n
θ
=
√
1
−
1
9
=
2
√
2
3
[
θ
is acute angle between
→
b
and
→
c
]
© examsnet.com
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