x and y are two mutually perpendicular unit vectors. If the vector ax + ay +c(x X y), x + (x X y) and cx + cy + b(x X y) lie in one plane, then c is

a) AM of a and b

b) GM of a and b

c) HM of a and b

d) equal to zero

Since the vectors lie in a plane,their triple product is zero.so,

det a a c   times[x y xXy]=0  this gives  (c²-ab)(xXy)²=0c is the G.M of a,b

      1 0 1

      c c b