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 line passing through the point (1, -5, 9) and parallel to x = y = z is
Thus, any point on this line is of the form
Now, if P(λ+1,λ−5,λ+9) is the point of intersection of line and plane, then
∴ Coordintes of point P are (-9, -15, -1).
Hence, required distance