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Let
\[
\Delta_{1}=\left|\begin{array}{ccc}
b^{2}+c^{2} & a b & a c \\
a b & c^{2}+a^{2} & b c \\
a c & b c & a^{2}+b^{2}
\end{array}\right|
\]
and
\[
\Delta_{2}=\left|\begin{array}{ccc}
-a^{2} & a b & a c \\
a b & -b^{2} & b c \\
a c & b c & -c^{2}
\end{array}\right|
\]
then
(a) \( \Delta_{1}+\Delta_{2}=0 \)
(b) \( \Delta_{1}=\Delta_{2} \)
(c) \( \Delta_{1}^{2}-\Delta_{2} \)
(d) \( \Delta_{1}-\Delta_{2}^{2} \)
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