Consider three planes $$\begin{aligned}
& P _ { 1 } : x - y + z = 1 \\
& P _ { 2 } : x + y - z = - 1 \\
& P _ { 3 } : x - 3 y + 3 z = 2 .
\end{aligned}$$ Let $L _ { 1 } , L _ { 2 } , L _ { 3 }$ be the lines of intersection of the planes $P _ { 2 }$ and $P _ { 3 } , P _ { 3 }$ and $P _ { 1 }$, and $P _ { 1 }$ and $P _ { 2 }$, respectively. STATEMENT-1: At least two of the lines $L _ { 1 } , L _ { 2 }$ and $L _ { 3 }$ are non-parallel. and STATEMENT-2 : The three planes do not have a common point. (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True
Consider three planes
$$\begin{aligned}
& P _ { 1 } : x - y + z = 1 \\
& P _ { 2 } : x + y - z = - 1 \\
& P _ { 3 } : x - 3 y + 3 z = 2 .
\end{aligned}$$
Let $L _ { 1 } , L _ { 2 } , L _ { 3 }$ be the lines of intersection of the planes $P _ { 2 }$ and $P _ { 3 } , P _ { 3 }$ and $P _ { 1 }$, and $P _ { 1 }$ and $P _ { 2 }$, respectively.
STATEMENT-1: At least two of the lines $L _ { 1 } , L _ { 2 }$ and $L _ { 3 }$ are non-parallel.\\
and\\
STATEMENT-2 : The three planes do not have a common point.\\
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\\
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\\
(C) STATEMENT-1 is True, STATEMENT-2 is False\\
(D) STATEMENT-1 is False, STATEMENT-2 is True