If the plane `2x-y+z=0` is parallel to the line `(2x-1)/2=(2-y)/2=(z+1)/a`, then the value of a is

Options

A. `-4`
B. `-2`
C. 4
D. 2

Answer

a

Explanation

The given line is `(x-1/2)/(1) = (y-2)/-2=(z-(-1))/a`.
The d.r.'s of the line are 1,-2,a.
The given plane is `2x-y+z=0`
The d.r.'s of the normal to this plane are 2,-1,1.
Since the given plane is parallel to the given line, so the normal to this plane is perpendicular to the given line.
`therefore (2 xx 1)-1xx(-2) +1 xx a =0 rArr a=-4`.