Let l, m, n be the direction ratios of the line L1.
Then l + m – n = 0
and l – 3m + 3n = 0
Thus,
Thus, the direction ratios of L1 are (0, 1, 1)
Similarly, the direction ratios of L2 and L3 are (0, 1, 1) and (0, 1, 1), respectively.
Therefore, the lines L1, L2 and L3 are parallel.
So, Statement I is false.
Put z = 0 in P2: x + y – z = – 1, P3: x – 3y + 3z = 2
we get,
does not lie on P1 , so no point of L1 lies on P1.
Therefore, the three planes do not have a common point.
Thus, the statement II is true.