A vector coplanar with vectors i+j and j+k and parallel to the vector 2i-2j-4k is. a)I-beama)i-kb)i-j-2kc)i+j-kd)3i+3j-6k

Dear Student,
let reqd vector is ai+bj+ck
as the 3 vectors ai+bj+ck, i+j , j+k are coplanar so one must be linear comination of other 2 i.e,
ai+bj+ck=x(i+j)+y(j+k)
=>ai+bj+ck=xi+(x+y)j+yk
from above a+c=b
also, ai+bj+ck is parallel to 2i-2j-4k,so 
ai+bj+ck=z(2i-2j-4k)
=>a=2z, b=-2z , c=-4z i.e. again we get a+c=b
option b) i-j-2k has a=1,b=-1,c=-2
so a+c=1-2=-1=b which satisfies a+c=b
so option(b)  i-j-2k is the answer.