If x(cap),y(cap),z(cap) are mutually perpendicular unit vectors and ax(cap)+ay(cap)+cz(cap),x(cap)+z(cap) and cx(cap)+cy(cap)+bz(cap) are coplanar,then

1. a,b,c are in A.P
2. a,b,c are in G.P
3. a,b,c are in H.P
4. a,c,b are in G.P

Since x,y,z are mutually perpendicular unit vectors we can consider then i,j,k..Now Write the Scalar triple product of the three vectors i.e; the determinent .. since they are coplanar put this determinent zero and get answer as c²=ab. Hence a,c,b are in GP