If the mirror image of the point 1 , 3 , 5 with respect to the plane 4 x - 5 y + 2 z = 8 is α , β , γ , then 5 α + β + γ equals :

Step-by-step solution

Point Q is image of point P w.r.to plane, M is mid point of P and Q , lies in plane M 1 + α 2 , 3 + β 2 , 5 + γ 2 4 x - 5 y + 2 z = 8 4 1 + α 2 - 5 3 + β 2 + 2 5 + γ 2 = 8     . . . 1 Also P Q perpendicualr to the plane ⇒ P Q → ‖ n → α - 1 4 = β - 3 - 5 = γ - 5 2 = k (let) α = 1 + 4 k β = 3 - 5 k γ = 5 + 2 k     . . . 2 use 2 in 1 2 1 + 4 k - 5 6 - 5 k 2 + 10 + 2 k = 8 k = 2 5 from 2 α = 13 5 , β = 1 ,