The point having position vector 4 i - 11 j + 2 k lies on the line

Step-by-step solution

Let the position vector of the given point be p = 4 i - 11 j + 2 k . All the given lines pass through the point with position vector a = 6 i - 4 j + 5 k . For the point to lie on the line r = a + b , the vector p - a must be a scalar multiple of the direction vector b . Calculating p - a : p - a = (4 i - 11 j + 2 k ) - (6 i - 4 j + 5 k ) p - a = -2 i - 7 j - 3 k = -1(2 i + 7 j + 3 k ) This shows that p - a is a scalar multiple of 2 i + 7 j + 3 k . Thus, the point lies on the line r = (6 i - 4 j + 5 k ) + (2 i + 7 j