Let a = j - k and c = i - j - k. Then the vector b satisfying a x b + c = 0 and a.b = 3 is

Let  a = j - k  and c = i - j - k. Then the vector b satisfying a x b + c = 0 and a.b = 3 is

  1. i - j - 2k
  2. i + j - 2k
  3. 2i - j + 2k
  4. -i + j - 2k

Solution

a x c = -2i - j - k

Given a x b + c = 0

a x (a x b) + a x c = 0

(a.b)a - (a.a)b + a x c = 0

3a - 2b + (-2i - j - k) = 0

2b = 3(j - k) + (-2i - j - k)

The correct option is D.