The distance between the planes `2x+2y-z+ 2=0\ a n d\ 4x+4y-2z+5=0` is `a. 1/2` b. `1/4'` c. `1/6` d. none of these

Explanation

Let point `Pleft(x_{1}, y_{1}, z_{1}right)` lie on plane `2 x+2 y+2 z=0`

` 2 x_{1}+2 y_{1}-z_{1}=-2`

` implies d=|frac{4 x_{1}+4 y_{1}-2 z_{1}+5}{sqrt{4^{2}+4^{2}+(-2)^{2}}}|

=|frac{2(2 x_{1}+2 y_{1}-z_{1})+5}{sqrt{16+16+4}}| `

`implies d=|frac{2(-2)+5}{sqrt{36}}|
=|frac{-4+5}{6}|
=frac{1}{6} text { unit }`


`therefore`So, option`(C)` is the correct answer.