Given point is A (1, 2, -2)

andequation of the line is  (x-1)/2 = (y+2)/1 = z/(-1)

Now any point B on the line is given by  {2x -(-1) , x - 2, -x }

 So B(2x + 1, x-2, -x)

Now AB = (2x + 1, x-2, x) -  (1, 2, -2)

             = (2x + 1 - 1, x-2-2, -x +2)

             = (2x , x-4, -x+2)

=> AB = 2x i + (x-4)j + (-x+2)k      

Since AB is perpendicular to (2i + j - k)

So AB.(2i + j - k) = 0

=> {2x i + (x-4)j + (-x+2)k}.(2i + j - k) = 0

=> 4x + x -4 - (-x+2) = 0

=> 4x + x -4 + x - 2 = 0

=> 6x - 6 = 0

=> 6x = 6

=> x = 6/6

=> x = 1

So AB =  2*1 i + (1-4)j + (-1+2)k

=> AB = 2i - 3j + k

Now |AB| = √(2² + 3² + 1)

=> |AB| = √(4 + 9 + 1)         

=> |AB = √14

So the distance is √14.

Hense option a is the correct answer