The given plane is x – y + z = 5 …… (1)

We have to find the distance of the point (1, – 5, 9) from this plane measured along a line to

x = y = z

So, the direction ratio of the line from the point (1, – 5, 9) to the given plane will be the same as that

of given line.

The equation of line passing through (1, – 5, 9) and having direction ratio is

x = r + 1, y = r – 5, z = r + 9

put in equation (1)

r + 1 – r + 5 + r + 9 = 5

⇒ r + 15 = 5

⇒ r = – 10

Coordinates are (–10 + 1, –10 – 5, –10 + 9) is (–9, –8, –1)

Distance of (–9, –15, –1) from (1, – 5, 9)

=