Given the line `L: (x-1)/(3) = (y+1)/(2) = (z +3)/(1)` and the plane `pi:x -2y + z=0,` of the following assertions, the only one that is always true is ,

Options

A. `L` is `_|_` to II
B. `L` lies in II
C. `L` is parallel to II
D. none of these

Answer

B

Explanation

We know that a line lies ina plane if every point on the line is a point on the plane. The coordinates of any point on line `L` are
`(3lamda+1,2lamdas-1,-lamda+3)`
Clearly, `3lamda+1-4lamda+2+lamda-3=0` i.e. the point `(3lamda+1,2lamda-1,-lamda+3)` lies on the plane II.
Hence the line `L` lies in the plane II.