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Mathematics
Mathematics
Problem
Let
a
⃗
,
b
⃗
,
c
⃗
\vec{a}, \vec{b}, \vec{c}
a
,
b
,
c
be three vectors such that
a
⃗
×
b
⃗
=
2
(
a
⃗
×
c
⃗
)
\vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c})
a
×
b
=
2
(
a
×
c
)
. If
∣
a
⃗
∣
=
1
|\vec{a}| = 1
∣
a
∣
=
1
,
∣
b
⃗
∣
=
4
|\vec{b}| = 4
∣
b
∣
=
4
,
∣
c
⃗
∣
=
2
|\vec{c}| = 2
∣
c
∣
=
2
, and the angle between
b
⃗
\vec{b}
b
and
c
⃗
\vec{c}
c
is
60
∘
60^\circ
6
0
∘
, then
∣
a
⃗
⋅
c
⃗
∣
|\vec{a} \cdot \vec{c}|
∣
a
⋅
c
∣
is equal to
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