The co-ordinates of the point in which line joining (1,1,1) and (2,2,2) intersects the plane x+y+z=9 are

Step-by-step solution

To determine where the line through (1,1,1) and (2,2,2) intersects the plane x+y+z=9 , parameterize the line using direction ratios proportional to the differences in coordinates: x = 1 + t , y = 1 + t , z = 1 + t . Substituting into the plane equation gives (1 + t) + (1 + t) + (1 + t) = 9 , which simplifies to 3 + 3t = 9 . Solving for t yields 3t = 6 and t = 2 . Substituting back provides the intersection point: x = 1 + 2 = 3 , y = 3 , z = 3 . The intersection occurs at (3,3,3) .