If O A ¯ = i ¯ + 2 j ¯ + 3 k ¯ and O B ¯ = 4 i ¯ + k ¯ are the position vectors of the points A and B , then the position vector of a point on the line passing through B and parallel to the vector O A ¯ × O B ¯ which is at a distance of 189 units from B is

Step-by-step solution

Let, C = x , y , z such that B C → is parallel to O A → × O B → and B C → = 189 . Apply B C → = λ O A → × O B → ⇒ x - 4 i ^ + y j ^ + z - 1 k ^ = λ i ^ j ^ k ^ 1 2 3 4 0 1 ⇒ x - 4 i ^ + y j ^ + z - 1 k ^ = λ 2 i ^ + 11 j ^ - 8 k ^ ⇒ x = 4 + 2 λ ,   y = 11 λ ,   z = 1 - 8 λ Apply B C → = 189 ⇒ 2 λ 2 + 11 λ 2 + - 8 λ 2 = 189 ⇒ λ = 1 So the position vector of the point C i