Perpendiculars are drawn from points on the line x + 2 2 = y + 1 - 1 = z 3 to the plane x + y + z = 3 . The feet of perpendiculars lie on the line

Step-by-step solution

The equation od given line is x + 2 2 = y + 1 - 1 = z 3 = λ Now any two points on this line are A - 2 , - 1 , 0 ,B 0 , - 2 , 3 for λ = 0 ,  1 Let foot of perpendicular from A ( - 2 , - 1 , 0 ) on plane is α ,  β ,  γ ⇒ α + 2 1 = β + 1 1 = γ - 0 1 = μ say Also the point lies on the plane, hence α + β + γ = 3 ⇒ μ - 2 + μ - 1 + μ = 3 ⇒ μ = 2 Hence the coordinates of M are ⇒ M 0, 1, 2 Similarly foot of