Let a = i + j , ~b =2 i - k , c =3 i - j + k , then vector p satisfying p a =0 and p b = c b is

Step-by-step solution

The condition p b = c b implies that ( p - c ) b = 0 , so p - c is parallel to b . Therefore, p = c + b for some scalar . Substituting the given c = 3 i - j + k and b = 2 i - k , we obtain: p = (3 + 2 ) i - j + (1 - ) k Applying the condition p a = 0 with a = i + j : (3 + 2 )(1) + (-1)(1) = 0 2 + 2 = 0 = -1 Substituting back: p = (3 - 2) i - j + (1 + 1) k = i - j + 2 k The result matches option D .