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Mathematics
Mathematics
Problem
If
a
,
b
\mathbf a, \mathbf b
a
,
b
and
c
\mathbf c
c
are three vectors such that
[
a
b
c
]
=
1
\left[\mathbf a\ \mathbf b\ \mathbf c\right]=1
[
a
b
c
]
=
1
, then find the value of
[
a
+
b
+
c
c
+
a
]
+
[
a
×
b
b
×
c
c
×
a
]
+
[
a
+
(
b
×
c
)
b
×
(
c
×
a
)
c
×
(
a
×
b
)
]
\left[\mathbf a+\mathbf b+\mathbf c\ \mathbf c+\mathbf a\right]+\left[\mathbf a\times\mathbf b\ \mathbf b\times\mathbf c\ \mathbf c\times\mathbf a\right]+\left[\mathbf a+(\mathbf b\times\mathbf c)\ \mathbf b\times(\mathbf c\times\mathbf a)\ \mathbf c\times(\mathbf a\times\mathbf b)\right]
[
a
+
b
+
c
c
+
a
]
+
[
a
×
b
b
×
c
c
×
a
]
+
[
a
+
(
b
×
c
)
b
×
(
c
×
a
)
c
×
(
a
×
b
)
]
.
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