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JEE Advanced 2016 Paper 2 Mathematics Q14
Mathematics
Problem
Let
u
^
=
u
1
i
^
+
u
2
j
^
+
u
3
k
^
\hat u=u_1\hat i+u_2\hat j+u_3\hat k
u
^
=
u
1
i
^
+
u
2
j
^
+
u
3
k
^
be a unit vector in
R
3
\mathbb R^3
R
3
and
w
^
=
1
6
(
i
^
+
j
^
+
2
k
^
)
\hat w=\dfrac{1}{\sqrt6}(\hat i+\hat j+2\hat k)
w
^
=
6
1
(
i
^
+
j
^
+
2
k
^
)
. Given that there exists a vector
v
⃗
\vec v
v
in
R
3
\mathbb R^3
R
3
such that
∣
u
^
×
v
⃗
∣
=
1
|\hat u\times\vec v|=1
∣
u
^
×
v
∣
=
1
and
w
^
⋅
(
u
^
×
v
⃗
)
=
1
\hat w\cdot(\hat u\times\vec v)=1
w
^
⋅
(
u
^
×
v
)
=
1
. Which of the following statement(s) is(are) correct?
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