The vectors x,y,z are linearly dependent iff they are coplanar iff

det 1 1 1  =0,on simplifying,we get b=1 and z=a²+b²=2a²=1a=1 or -1.

      4 3 4

     1 a b

Hence the ans is option 4.

[I think u might have typed c instead of z in the question]