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Mathematics
Mathematics
Problem
If
b
\mathbf{b}
b
and
c
\mathbf{c}
c
are two non-collinear vector such that
a
∥
(
b
×
c
)
\mathbf{a} \parallel (\mathbf{b} \times \mathbf{c})
a
∥
(
b
×
c
)
, then prove that
(
a
×
b
)
⋅
(
a
×
c
)
(\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{a} \times \mathbf{c})
(
a
×
b
)
⋅
(
a
×
c
)
is equal to
∣
a
∣
2
(
b
⋅
c
)
|\mathbf{a}|^2 (\mathbf{b} \cdot \mathbf{c})
∣
a
∣
2
(
b
⋅
c
)
.
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