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Mathematics
Mathematics
Problem
Let
v
=
2
i
^
+
j
^
−
k
^
\mathbf{v} = 2\hat{i} + \hat{j} - \hat{k}
v
=
2
i
^
+
j
^
−
k
^
and
w
=
i
^
+
3
k
^
\mathbf{w} = \hat{i} + 3\hat{k}
w
=
i
^
+
3
k
^
. If
u
^
\hat{u}
u
^
is unit vector and the maximum value of
[
u
v
w
]
=
λ
[\mathbf{u} \mathbf{v} \mathbf{w}] = \sqrt{\lambda}
[
uvw
]
=
λ
, then the value of
(
λ
−
51
)
(\lambda - 51)
(
λ
−
51
)
is
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