Consider a plane `P-=2x+y-z-=0` a line `(x-3)/2=(y+1)/(-3)=(z-2)/(-1)` and a point `A(3,-4,1)`. `L_(2)` is a line passing through `A` intersecting `L_(1)` an parallel to the plane `P`
Plane containing `L_(1)` and `L_(2)` is

Options

A. Parallel to `yz` plane
B. Paralel to `x` -axis
C. Parallel to `y`-axis
D. Passing through origin

Answer

A

Explanation

Equation of line `L_(2)` is `(x-3)/1=(y+4)/(-3)=(z-1)/(-1)`
(1) Equation of plane containing `L_(1)` & `L_(2)`
`|(x-3, y+1, z-2),(0,3,1),(-1,6,2)|=0implies+3z-5=0`
(2) Volume of tetrahedron `=1/6 |(3,-4,1),(5,-4,1),(7,-7,0)|=7/3`