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Mathematics
Mathematics
Problem
If
a
,
b
\mathbf{a}, \mathbf{b}
a
,
b
and
c
\mathbf{c}
c
are any three vectors in space, then show that
(
c
+
b
)
×
(
c
+
a
)
⋅
(
c
+
b
+
a
)
=
[
a
b
c
]
(\mathbf{c} + \mathbf{b}) \times (\mathbf{c} + \mathbf{a}) \cdot (\mathbf{c} + \mathbf{b} + \mathbf{a}) = [\mathbf{a} \mathbf{b} \mathbf{c}]
(
c
+
b
)
×
(
c
+
a
)
⋅
(
c
+
b
+
a
)
=
[
abc
]
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