If the foot of the perpendicular drawn from 1 , 9 , 7 to the line passing through the point 3 , 2 , 1 and parallel the planes x + 2 y + z = 0 and 3 y - z = 3 is α , β , γ , then α + β + γ is equal to

Step-by-step solution

We know that, Direction ratio of line parallel the planes x + 2 y + z = 0 and 3 y - z = 3 is given by, D . R = i ^ j ^ k ^ 1 2 1 0 3 - 1 = - 5 i ^ + j ^ + 3 k ^ Now given line is passing through 3 , 2 , 1 and having direction ratio - 5 , 1 , 3 , So, equation of line will be x - 3 - 5 = y - 2 1 = z - 1 3 = t Now let any point line is given by Q ≡ - 5 t + 3 ,   t + 2 ,   3 t + 1 Now we need to find foot of perpendicular from point P 1 , 9 , 7 , So direction ratio of line Q P will be - 5 t + 3 - 1 , &#