Let P be a point on the line L₁: x-2 2 = y + 1 = z-1 2 such that its distance from the point A(2 , -1 , 1) is 6 units. Given that x -coordinate of P is greater than 2 , Find the coordinates of point Q on the line L₂: x - 1 = y-2 2 = z-2 2 such that Q is the closest point to P .

Step-by-step solution

The line L₁ is given by x-2 2 = y+1 1 = z-1 2 . The direction ratios of L₁ are (2, 1, 2) , so its direction cosines are ( 2 3 , 1 3 , 2 3 ) . The point A is (2, -1, 1) , which lies on L₁ . Since P is at a distance of 6 units from A , the coordinates of P are given by: (2 6 ( 2 3 ), -1 6 ( 1 3 ), 1 6 ( 2 3 ) ) Since the x -coordinate of P is greater than 2 , we take the positive sign: P = (2 + 4, -1 + 2, 1 + 4) = (6, 1, 5) The line L₂ is given by x-1 1 = y-2 2 = z-2 2 . Let Q be a point on L₂ . Its coordinates can b