A set of vector \( \left\{\left(a_{1}, a_{2}, a_{3}\right),\left(b_{1}, b_{2}, b_{3}\right),\left(c_{1}, c_{2}, c_{3}\right)\right\} \) is said to be linearly independent if and only if
\[
\left|\begin{array}{lll}
a_{1} & a_{2} & a_{3} \\
b_{1} & b_{2} & b_{3} \\
c_{1} & c_{2} & c_{3}
\end{array}\right| \neq 0,
\]
otherwise the set is said to be linearly dependent.
A similar result holds for \( \left\{\left(a_{1}, a_{2}\right),\left(b_{1}, b_{2}\right)\right\} \).
If \( A B C \) is a triangle, then the vectors
\( -(-1, \cos C, \cos B),(\cos C,-1, \cos A) \) and \( (\cos B \), \( \cos C,-1) \) are
(a) linearly independent for all triangles
(b) linearly dependent for all triangles
(c) linearly independent for all isosceles triangles
(d) none of these
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