Statement 1: The plane `5x+2z-8=0` contains the line `2x-y+z-3=0` and `3x+y+z=5`, and is perpendicular to `2x-y-5z-3=0`. Statement 2: The plane `3x+y+z=5`, meets the line `x-1=y+1=z-1` at the point (1,1,1)

Options

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.

Answer

C

Explanation

The equation of the family of planes containing the line `2x-y+z-3=0,3x+y+z=5` is
`2x-y+z-3+lamda(3x+y+z-5)=0`
For `lamda=1` this reduces to `5x+2z-8=0`
So the plane `5x+2z-8=0` contains the given line.
Also `2xx5-1xx0-5xx2=0`
So, the plane `5x+2z-8=0` is perpendicular to
`2x-y-5z-3=0`
Hence, statement -1 is true.
The coordinate of any point on line `(x-1)/1=(y+1)/1=(z-1)/1` are `(r+1,r-1,r+1)`.
If this point lies on the plane `3x+y+z=5`. Then,
`3r+3r-1+r+1=5impliesr=2/5`
Thus, the line meets the plane at `(7/5,-3/5,7/5)`
So, Statemnet -2 is not true.