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 \( a, b, c \) are distinct and \( \left(a, a^{2}, a^{3}+1\right),\left(b, b^{2}, b^{3}+1\right) \), \( \left(c, c^{2}, c^{3}+1\right) \) are linearly dependent, then value of \( a b c \) is
(a) \( -1 \)
(b) \( -2 \)
(c) 2
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