If the equation of plane passing through the mirror image of a point 2 , 3 , 1 with respect to line x + 1 2 = y - 3 1 = z + 2 - 1 and containing the line x - 2 3 = 1 - y 2 = z + 1 1 is α x + β y + γ z = 24 then α + β + γ is equal to:

Step-by-step solution

The given line is x + 1 2 = y - 3 1 = z + 2 - 1 x + 1 2 = y - 3 1 = z + 2 - 1 = λ   ( let ) ⇒ x + 1 2 = λ ,   y - 3 1 = λ ,   z + 2 - 1 = λ ⇒ x = 2 λ - 1 ,   y = λ + 3 ,   z = - λ - 2 Hence, any point on the line x + 1 2 = y - 3 1 = z + 2 - 1 is 2 λ - 1 ,   λ + 3 ,   - λ - 2 . Let, M be the foot of perpendicular from the point P to the line x + 1 2 = y - 3 1 = z + 2 - 1 , hence M ≡ 2 λ - 1 ,   λ + 3