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 $\mathrm{L}_1, \mathrm{~L}_2$ and $\mathrm{L}_3$ are non-parallel.
and
STATEMENT -2: The three planes do not have a common point.
Select the correct option:
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
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
The direction cosines of each of the lines $\mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3$ are proportional to $(0,1,1)$.
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