Consider three planes `P_(1):x-y+z=1`
`P_(2):x+y-z=-1`
and `" "P_(3):x-3y+3z=2`
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),P_(1)` and `P_(2)` respectively.
Statement I Atleast two of the lines `L_(1),L_(2)` and `L_(3)` are non-parallel.
Statement II The three planes do not have a common point.

Options

A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.
C. Statement 1 is true and Statement 2 is false.
D. Statement 1 is false and Statement 2 is true.

Answer

d

Explanation

The direction cosines of each of the lines `L_(1), L_(2), L_(3)` are proportional to `(0, 1, 1)`.