The vectors a, b, c are of same length and the angle between any two of them is same.

a=(i + j), b=(j+k), then c is?

i +k.

to understand this.

draw a cube whose three edges are x y and z axes.(do this on paper)

the vectors i +j and j+k are two diagonals. the third diagonal would have to be along i + k.

(note that vectors can be moved around anywhere parallel to themselves, so there is no real fixed position)

am i right?

Alter method,let c=xi+yj+zk,given a=b=c(mod)=rt2  and a.b=b.c=c.a(since the angle between them is zero)=1.This gives x+y=y+z=1 which means x=z=1&y=0