The line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ cuts the plane $x + y + z = 17 $ at

(3, 4, 5) (4, 6, 7) (4, 5, 8) (8, 4, 5)

(4, 6, 7)

The coordinates of any point on the given line are given by  $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}=λ$ Suppose the givem line cuts the given plane at (λ+3,2λ+4, 2λ + 5). This lies on the plane. $ ∴ λ+3+ 2λ+4+2λ+5 = 17 ⇒ λ = 1 $ Hence, the coordinates of the required point are (4, 6, 7).