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Mathematics
Mathematics
Problem
Let
a
,
b
\mathbf{a}, \mathbf{b}
a
,
b
and
c
\mathbf{c}
c
be three mutually perpendicular vectors of equal magnitude. If the vector
x
\mathbf{x}
x
satisfies the equation
a
×
{
(
x
−
b
)
×
a
}
+
b
×
{
(
x
−
c
)
×
b
}
+
c
×
{
(
x
−
a
)
×
c
}
=
0
\mathbf{a} \times \{(\mathbf{x} - \mathbf{b}) \times \mathbf{a}\} + \mathbf{b} \times \{(\mathbf{x} - \mathbf{c}) \times \mathbf{b}\} + \mathbf{c} \times \{(\mathbf{x} - \mathbf{a}) \times \mathbf{c}\} = 0
a
×
{(
x
−
b
)
×
a
}
+
b
×
{(
x
−
c
)
×
b
}
+
c
×
{(
x
−
a
)
×
c
}
=
0
, then find
x
\mathbf{x}
x
.
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