The vectors a and b are not perpendicular

The vectors a and b are not perpendicular and c and d are two vectors satisfying: b x c = b x d and a.d = 0. Then the vector d is equal to

  1. b - (b.c/a.d)c
  2. c + (a.c/a.b)b
  3. c - (a.c/a.b)b
  4. b - (b.c/a.d)c

Answer

a.b = 0, b x c = b x d, a.d = 0

(b x c) x a = (b x d) x a

(b.a)c - (c.a)b = (b.a)d - (d.a)b

The correct option is C.