The distance of the point having position vector - i ^ + 2 j ^ + 6 k ^ from the straight line passing through the point 2 , 3 , - 4 and parallel to the vector, 6 i ^ + 3 j ^ - 4 k ^ is

Step-by-step solution

Let, the given point be P ≡ - i ^ + 2 j ^ + 6 k ^ and A ≡ 2 ,   3 ,   - 4 , hence the position vector of the point A is 2 i ^ + 3 j ^ - 4 k ^ . We know that the vector joining two points x 1 ,   y 1 ,   z 1 and x 2 ,   y 2 ,   z 2 is x 2 - x 1 i ^ + y 2 - y 1 j ^ + z 2 - z 1 k ^ , Hence, the vector A P → = - 1 - 2 i ^ + 2 - 3 j ^ + 6 + 4 k ^ ⇒ A P → = - 3 i ^ - j ^ + 10 k ^ And, A D is the projection of A P → on the given line i.e. 6 i ^ + 3 j ^ - 4