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If the plane 2x-y+z=0 is parallel to the...

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

A

4

B

`-4`

C

2

D

`-2`

Text Solution

Verified by Experts

The correct Answer is:
B
Given line can be rewritten as
`(x-(1)/(2))/(1)=(y-2)/(-2)=(z+1)/(a)`
If any line is parallel to the plane, then `a_(1)a_(2)+b_(a)b_(2)+c_(1)c_(2)=0`
Here DR's of plane `(a_(1),b_(1)c_(1))=(2,-1,1)`
and DR's of a line `(a_(2),b_(2),c_(2))=(1,-2,a)`
`:." "2(1)-2(-1)+a(1)=0`
`rArr" "a=-4`
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