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Consider three planes P1 : x-y + z = 1, ...

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` and `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 . Statement 2:The three planes do not have a common point

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.

Text Solution

Verified by Experts

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