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Consider the following linear equations \( a x+b y+c z=0 \) \( b x+c y+a z=0 \) and \( c x+a y+b z=0 \)

Match the conditions / expressions in Coloum-I with statements in Column-II.
\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{\( \begin{array}{c}\text { Column-I } \\
\text { (Function) }\end{array} \)} & \multicolumn{2}{c|}{\( \begin{array}{c}\text { Column-II } \\
\text { (Period) }\end{array} \)} \\
\hline A. & \( \begin{array}{l}a+b+c \neq 0 \text { and } a^{2}+b^{2} \\
+c^{2}=a b+b c+c a\end{array} \) & p. & \( \begin{array}{l}\text { The equations represent } \\
\text { planes meeting at one } \\
\text { point }\end{array} \) \\
\hline B. & \( \begin{array}{l}a+b+c=0 \text { and } a^{2}+b^{2} \\
+c^{2} \neq a b+b c+c a\end{array} \) & q. & \( \begin{array}{l}\text { The equations represent } \\
\text { the line } x=y=z .\end{array} \) \\
\hline C. & \( \begin{array}{l}a+b+c \neq 0 \text { and } a^{2}+b^{2} \\
+c^{2} \neq a b+b c+c a\end{array} \) & r. & \( \begin{array}{l}\text { The equations represent } \\
\text { identical planes. }\end{array} \) \\
\hline D. & \( \begin{array}{l}a+b+c=0 \text { and } a^{2}+b^{2} \\
+c^{2}=a b+b c+c a\end{array} \) & s. & \( \begin{array}{l}\text { The equations represent } \\
\text { the whole of the three } \\
\text { dimensional space. }\end{array} \) \\
\hline
\end{tabular}
(a) \( \mathrm{A} \rightarrow \) (s), B \( \rightarrow \) (p), C \( \rightarrow \) (q), D \( \rightarrow \) (r)
(b) \( \mathrm{A} \rightarrow \) (p), B \( \rightarrow \) (q), C \( \rightarrow \) (s), \( \mathrm{D} \rightarrow \) (r)
(c) \( \mathrm{A} \rightarrow \) (r), \( \mathrm{B} \rightarrow \) (q), \( \mathrm{C} \rightarrow(\mathrm{p}), \mathrm{D} \rightarrow \) (s)
(d) \( \mathrm{A} \rightarrow \) (r), \( \mathrm{B} \rightarrow \) (q), \( \mathrm{C} \rightarrow(\mathrm{s}), \mathrm{D} \rightarrow \) (p)
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