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AIEEE 2007 Solved Paper
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© examsnet.com
Question : 111
Total: 118
If
∧
u
and
∧
v
are unit vectors and
θ
is the acute angle between them, then
2
∧
u
×
3
∧
v
is a unit vector for
no value of
θ
exactly one value of
θ
exactly two values of
θ
more than two values of
theta
Validate
Solution:
Given
|
2
∧
u
×
3
∧
v
|
=
1
and
θ
is acute angle between
∧
u
and
∧
v
,
|
∧
u
|
=
1
,
|
∧
v
|
=
1
⇒
6
|
∧
u
|
|
∧
v
|
|
s
i
n
θ
|
=
1
⇒
6
|
s
i
n
θ
|
=
1
⇒
s
i
n
θ
=
1
6
Hence, there is exactly one value of
θ
for which
2
∧
u
×
3
∧
v
is a unit vector.
© examsnet.com
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