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Mathematics
Mathematics
Problem
If
A
,
B
\mathbf{A}, \mathbf{B}
A
,
B
and
C
\mathbf{C}
C
are vectors such that
∣
B
∣
=
∣
C
∣
|\mathbf{B}| = |\mathbf{C}|
∣
B
∣
=
∣
C
∣
, prove that
{
(
A
+
B
)
×
(
A
+
C
)
}
×
(
B
×
C
)
⋅
(
B
+
C
)
=
0.
\{(\mathbf{A} + \mathbf{B}) \times (\mathbf{A} + \mathbf{C})\} \times (\mathbf{B} \times \mathbf{C}) \cdot (\mathbf{B} + \mathbf{C}) = 0.
{(
A
+
B
)
×
(
A
+
C
)}
×
(
B
×
C
)
⋅
(
B
+
C
)
=
0.
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