The distance of the point (1, 5, 9) from the plane x - y + z = 5 measured along the line x = y = z is:

Equation of the line x - 1 = y + 5 = z - 9 = λ
The co-ordinates of the point is (λ + 1, λ - 5, λ + 9)
Substitute the co-ordinates in the equation of the plane x - y + z = 5
λ + 1 - (λ - 5) + λ + 9 = 5
λ = -10
One point = (1, -5, 9)
Other point = (-9, -15, -1)
Distance between the two points = √((-9 - 1)² + (-15 + 5)² + (-1 - 9)²)
= √(100 + 100 + 100) = 10√3