If the vectors \(\vec{\alpha}=\hat{i}+a \hat{j}+a^{2} \hat{k}, \vec{\beta}=\hat{i}+b \hat{j}+b^{2} \hat{k}\), and \(\vec{\gamma}=\hat{i}+c \hat{j}+c^{2} \hat{k}\) are three non-coplanar vectors and \(\left|\begin{array}{lll}a & a^{2} & 1+a^{3} \\ c & c^{2} & 1+b^{3}\end{array}\right|=0\),
then the value of abc is
\(\begin{array}{llll}\text { (A) } 1 & \text { (B) } 0 & \text { (C) }-1 & \text { (D) } 2\end{array}\)
